Document [original]

Essays in Experimental Industrial Organization

on Economic Issues of the Digital Age

vorgelegt von

Michel Tolksdorf, M.Sc.

ORCID: 0000-0001-9825-6992

an der Fakultät VII – Wirtschaft und Management

der Technischen Universität Berlin

zur Erlangung des akademischen Grades

Doktor der Wirtschaftswissenschaften

– Dr. rer. oec. –

genehmigte Dissertation

Promotionsausschuss:

Vorsitzender: Prof. Dr. Tomaso Duso

Gutachterin: Prof. Dr. Radosveta Ivanova-Stenzel

Gutachterin: Prof. Dr. Dorothea Kübler

Tag der wissenschaftlichen Aussprache: 04. September 2023

Berlin, 2023

Abstract

Digitization shapes many aspects of our everyday life, including professional and

social interactions, knowledge acquisition and dissemination, cultural exchange, en-

tertainment, and – last but not least – economic activities. Accordingly, digitization

has caused a shift in some strands of the economic literature. Studies in industrial

organization incorporate potentially biased consumer behavior and reflect techno-

logical advances such as history-based price discrimination, data brokerage, multi-

sided platforms, and personalized advertisements, among others. Given that we face

a vast range of impacts of digitization on economics and markets, this dissertation

focuses on some key aspects. Using methods of theoretical industrial organization

and experimental behavioral economics, this dissertation tackles issues of price dis-

crimination, privacy concern and crowdfunding. First, I provide a methodological

contribution, reassessing what inferences can be drawn on behavior-based pricing

tools from laboratory market experiments. I find that price distortions can be ex-

plained but not necessarily circumvented. Second, drawing from the insights of the

first study, we theoretically and experimentally study a richer framework, incorpo-

rating endogenous privacy choices for consumers in two data environments. An open

data environment where consumers’ purchasing histories are readily available to all

firms benefits consumers at the cost of total welfare compared to an exclusive data

environment where firms individually hold information over purchasing histories,

i.e., the current status quo. Lastly, we study how innate coordination problems of

reward-based crowdfunding mechanisms can be remedied. We find that rebates are

a suitable and easy-to-use tool that improves the success rate of projects, as backers

are willing to pledge higher amounts.

Keywords: Behavior-based pricing, crowdfunding, forward-looking customers, lab-

oratory experiment, myopic customers, privacy, provision point mechanism, rebates,

reference dependence

Zusammenfassung

Digitalisierung prägt viele Aspekte unseres täglichen Lebens, darunter berufliche und

soziale Interaktionen, Wissenserwerb und -verbreitung, kultureller Austausch, Un-

terhaltung und nicht zuletzt wirtschaftliche Aktivitäten. Dementsprechend hat die

Digitalisierung in einigen Bereichen der Wirtschaftsliteratur einen Wandel bewirkt.

Studien der Industrieökonomik berücksichtigen potenziell verzerrtes Verbraucherver-

halten und reflektieren technologische Fortschritte, wie z.B. Preisdiskriminierung

basierend auf Kaufhistorien, Datenvermittlung, mehrseitige Plattformen und per-

sonalisierte Werbung. Da die Auswirkungen der Digitalisierung auf Wirtschaft und

Märkte sehr vielfältig sind, konzentriert sich diese Dissertation auf einige zentrale

Aspekte. Unter Verwendung von Methoden der theoretischen Industrieökonomik

und der experimentellen Verhaltensökonomie befasst sich diese Dissertation mit Fra-

gen der Preisdiskriminierung, des Datenschutzes und des Crowdfunding. Zunächst

leiste ich einen methodischen Beitrag, indem ich neu bewerte, welche Rückschlüsse

aus Laborexperimenten auf verhaltensbasierte Preisbildung gezogen werden kön-

nen. Ich stelle fest, dass Preisverzerrungen zwar erklärt, aber nicht unbedingt um-

gangen werden können. Zweitens untersuchen wir, aufbauend auf den Erkenntnis-

sen der ersten Studie, theoretisch und experimentell einen umfassenderen Rahmen,

der endogene Datenschutzentscheidungen der Konsumierenden in zwei Datenumge-

bungen einbezieht. Eine Umgebung offener Daten, in der die Kaufhistorien der

Konsumierenden allen Unternehmen zur Verfügung steht, bringt den Konsumieren-

den Vorteile auf Kosten der Gesamtwohlfahrt im Vergleich zu einer Umgebung

exklusiver Daten, in der die Unternehmen individuell über die Informationen der

Kaufhistorien verfügen, d.h. dem derzeitigen Status quo. Schließlich untersuchen

wir, wie inhärente Koordinationsprobleme von vergütungsbasierten Crowdfunding-

Mechanismen behoben werden können. Wir stellen fest, dass Rückzahlungen ein

geeignetes und einfach zu handhabendes Instrument sind, das die Erfolgsquote von

Projekten erhöht, da Unterstützende bereit sind, höhere Beträge zu leisten.

Schlüsselwörter: Crowdfunding, Datenschutz, Laborexperiment, naive Konsum-

ierende, Provision-point-Mechanismus, Referenzabhängigkeit, Rückzahlungen, ver-

haltensbasierte Preisbildung, vorausschauende Verbraucher

Acknowledgements

I wrote this dissertation during my time as a research associate at Technische Uni-

versität Berlin. During this time, I was part of the Collaborative Research Center

Transregio “Rationality and Competition” funded by the German Research Founda-

tion, to whom I give credit for having financed a large part of the research for my

dissertation.

First of all, I would like to thank Radosveta Ivanova-Stenzel for her continuous

support. At times I needed a nudge, and at other times I needed a push, both of

which she provided when necessary. Similarly, I thank Dorothea Kübler, whom I em-

blematically associate with the whole Berlin Behavioral Economics (BBE) group.

I can safely say that without Radosveta Ivanova-Stenzel and Dorothea Kübler, I

would never have ventured into experimental economics.

Next, I want to thank my co-authors, colleagues and office mates: Fabian Ger-

stmeier, Friederike Heiny, Maximilian Kellner, Pauline Affeldt, Tianchi Li, Tim

Hainbach, Vera Angelova, Vincent Meisner, and Yigit Oezcelik. Thanks to them,

I learned that the most valuable thing about a doctorate is the friends you make

along the way.

My love and my last thanks go to my family and friends, and my partner in life,

love, and everything that matters, Bianca Faber.

iii

Rechtliche Erklärung

Hiermit versichere ich, dass ich die vorliegende Dissertation selbstständig und ohne

unzulässige Hilfsmittel verfasst habe. Die verwendeten Quellen sind vollständig im

Literaturverzeichnis angegeben. Die Arbeit wurde noch keiner Prüfungsbehörde in

gleicher oder ähnlicher Form vorgelegt.

Berlin, 01. Juni 2023

Michel Tolksdorf

Overview of Included Publications

Tolksdorf, M. (2023). On Point Predictions and Reference Dependence in Behavior-

Based Pricing Experiments. Journal of Economics and Behavioral Studies, 15(1(J),

1-14. https://doi.org/10.22610/jebs.v15i1(J).3340 (Published version).

Heiny, F., Li, T., and Tolksdorf, M. (2023). We Value Your Privacy: Behavior-

based Pricing Under Endogenous Privacy. Available at SSRN 3508762.https:

//doi.org/10.2139/ssrn.3508762 (Working paper).

Gerstmeier, F., Oezcelik, Y., and Tolksdorf, M. (2023). Rebate Rules in Reward-

Based Crowdfunding: Introducing the Bid-Cap Rule. Collaborative Research

Center Transregio 190, Discussion Paper No. 392. https://doi.org/10.5282/

ubm/epub.95542 (Discussion paper).

Contents

List of Tables viii

List of Figures x

1 General Introduction 1

1.1 Economic Issues of the Digital Age . . . . . . . . . . . . . . . . . . . 1

1.2 Outline of the Dissertation . . . . . . . . . . . . . . . . . . . . . . . . 4

1.2.1 On Point Predictions in Behavior-based Pricing Experiments . 4

1.2.2 Behavior-based Pricing Under Endogenous Privacy . . . . . . 5

1.2.3 Rebate Rules in Reward-based Crowdfunding . . . . . . . . . 6

2 On Point Predictions in Behavior-based Pricing Experiments 7

2.1 Introduction................................ 7

2.2 An Experiment on Uniform and Behavior-based Pricing . . . . . . . . 9

2.2.1 Theoretical Background . . . . . . . . . . . . . . . . . . . . . 10

2.2.2 Experimental Design . . . . . . . . . . . . . . . . . . . . . . . 12

2.2.3 Results............................... 13

2.3 Reference Dependence Impacts Second-Period Prices . . . . . . . . . 16

2.3.1 Theoretical Preamble . . . . . . . . . . . . . . . . . . . . . . . 17

2.3.2 Experimental Follow-up . . . . . . . . . . . . . . . . . . . . . 18

2.3.3 Findings.............................. 19

2.4 Myopic Consumers Induce Lower First-period Prices . . . . . . . . . 20

2.5 Transport Costs as a Robust Welfare Measure . . . . . . . . . . . . . 22

2.6 Conclusion................................. 24

2.7 Translated Instructions and Review Questions . . . . . . . . . . . . . 25

3 We Value Your Privacy: Behavior-based Pricing Under Endoge-

nous Privacy 34

3.1 Introduction................................ 34

3.1.1 Related Literature . . . . . . . . . . . . . . . . . . . . . . . . 37

3.2 Theory................................... 40

3.2.1 Model ............................... 40

3.2.2 Endogenous Privacy . . . . . . . . . . . . . . . . . . . . . . . 42

3.2.3 Welfare .............................. 51

3.3 Experiment ................................ 53

3.3.1 Design............................... 53

3.3.2 Hypotheses ............................ 57

3.3.3 Results............................... 58

3.4 Conclusion and Discussion . . . . . . . . . . . . . . . . . . . . . . . . 68

3.5 Appendix – Theoretical Part . . . . . . . . . . . . . . . . . . . . . . . 70

3.6 Appendix – Experimental Part . . . . . . . . . . . . . . . . . . . . . 84

4 Rebate Rules in Reward-based Crowdfunding: Introducing the

Bid-cap Rule 96

4.1 Introduction................................ 96

4.2 TheGame................................. 99

4.3 TheExperiment..............................103

4.3.1 Experimental Design and Procedures . . . . . . . . . . . . . . 103

4.3.2 Hypotheses ............................105

4.4 Results...................................106

4.5 Conclusion.................................111

4.6 Appendix .................................113

4.6.1 Proof of negative marginal penalty of over-contribution . . . . 113

4.6.2 Proof that a solution for the bid-cap rule must exist . . . . . . 113

4.6.3 Proof that the solution in 4.6.2 is unique . . . . . . . . . . . . 115

4.6.4 Proof of payment relation of bid-cap and proportional rebate

for a discrete sequence of pledges . . . . . . . . . . . . . . . . 115

4.6.5 Additional regressions . . . . . . . . . . . . . . . . . . . . . . 117

4.6.6 Additional figures . . . . . . . . . . . . . . . . . . . . . . . . . 119

4.6.7 Translated instructions . . . . . . . . . . . . . . . . . . . . . . 122

5 Concluding Remarks 132

vii

List of Tables

2.1 Comparison of price predictions. . . . . . . . . . . . . . . . . . . . . . 12

2.2 Comparison of observed prices. . . . . . . . . . . . . . . . . . . . . . 14

2.3 Comparison of price effects. . . . . . . . . . . . . . . . . . . . . . . . 14

2.4 Analysis of prices between treatments. . . . . . . . . . . . . . . . . . 15

2.5 Regressions on difference between observed and predicted prices per

roundandtreatment............................ 16

2.6 Observed prices (follow-up). . . . . . . . . . . . . . . . . . . . . . . . 20

2.7 Treatment effects on welfare measures in the first and second period. 23

2.8 Sum of mean profits, total costs and transport costs between cases. . 23

3.1 Prices visible to buyers according to purchase and tracking decision. ...... 55

3.2 Summary statistics for pricing choices of sellers. . . . . . . . . . . . . 59

3.3 Summary statistics for purchasing and privacy choices of buyers. . . . 60

3.4 Price differences within treatments. . . . . . . . . . . . . . . . . . . . 62

3.5 Price differences between treatments. . . . . . . . . . . . . . . . . . . 62

3.6 Observed and adjusted price predictions under pooling assumption. . 63

3.7 Share of purchases from the far seller at equal total costs. . . . . . . . 64

3.8 Impact of learning on tracking decision. . . . . . . . . . . . . . . . . . 65

3.9 Effects of treatment and privacy choice on switching, poaching and

retainingofbuyers............................. 66

3.10 Effects of treatment on buyer’s transportation costs in first, second

andbothperiods.............................. 67

3.11 Share of purchasing orders and information disclosure by treatment

andlocation. ............................... 94

viii

3.12 Impact of treatment, tracking and learning on purchasing decision

when total costs are equal. . . . . . . . . . . . . . . . . . . . . . . . . 94

3.13 Interaction between privacy concern and learning. . . . . . . . . . . . 95

4.1 Summary statistics with standard deviations in brackets. . . . . . . . 107

4.2 Analysis of treatment effects on pledges and the successful realization

ofprojects. ................................109

4.3 Analysis of pledges compared to the equilibrium prediction within

experimental treatments. . . . . . . . . . . . . . . . . . . . . . . . . . 117

4.4 Analysis of pledges compared to valuation within experimental treat-

ments. ...................................117

4.5 Analysis of pledges compared to the equilibrium prediction and the

valuation within experimental treatments with Part 1 & Part 2 pooled.118

4.6 Analysis of treatment effects on pledges and the realization of projects

with Part 1 & Part 2 pooled . . . . . . . . . . . . . . . . . . . . . . . 118

List of Figures

2.1 Comparison of distribution of prices . . . . . . . . . . . . . . . . . . . 15

2.2 Distribution of prices (follow-up). . . . . . . . . . . . . . . . . . . . . 20

3.1 Timelineofthegame............................ 42

3.2 consumer segments under open data in t= 2. ............. 44

3.3 consumer segments under exclusive data. . . . . . . . . . . . . . . . . 48

3.4 Prices of Firm Afor ¯

θ= 1 and θ1= 0.5. ................ 50

3.5 Conversion of theoretical into experimental market. . . . . . . . . . . 54

3.6 Fraction of buyers who share their data over rounds by treatment. . . 64

3.7 Observed and predicted average transportation costs per round. . . . 66

3.8 Total costs in equilibrium (solid) and for individual deviators (dotted). 73

3.9 Line with multiple segments in case (i). . . . . . . . . . . . . . . . . . 73

3.10 Line with two segments in case (i). . . . . . . . . . . . . . . . . . . . 75

3.11 Line with multiple segments in case (ii). . . . . . . . . . . . . . . . . 75

3.12 Line with two segments in case (ii). . . . . . . . . . . . . . . . . . . . 76

3.13 Total costs in equilibrium (solid) and for individual deviators (dotted). 80

3.14 Line with multiple segments in case (i). . . . . . . . . . . . . . . . . . 81

3.15 Line with two segments in case (i). . . . . . . . . . . . . . . . . . . . 82

3.16 Line with multiple segments in case (ii). . . . . . . . . . . . . . . . . 82

3.17 Line with two segments in case (ii). . . . . . . . . . . . . . . . . . . . 83

3.18 Representation of the Game of 22. . . . . . . . . . . . . . . . . . . . . 88

3.19 Share of tracking allowed over periods by Treatment and privacy con-

cern..................................... 90

3.20 Share of tracking allowed per location by Treatment and privacy con-

cern..................................... 91

3.21 Game of 22 scores by Treatment. . . . . . . . . . . . . . . . . . . . . 92

3.22 IUIPC scores by Treatment. . . . . . . . . . . . . . . . . . . . . . . . 92

3.23 Observed and predicted prices in the open data treatment. . . . . . . 93

3.24 Observed and predicted prices in the exclusive data treatment. . . . . 93

4.1 An example of payments by pledge under rebate rules. . . . . . . . . 102

4.2 Distribution of pledges (classified). . . . . . . . . . . . . . . . . . . . 108

4.3 Pledge to payment mapping of funded projects in rebate rule treat-

ments. ...................................109

4.4 Cumulative distribution of pledges (top) and kernel density estima-

tion of pledges (bottom) by experimental treatment. . . . . . . . . . . 119

4.5 Cumulative distribution of pledges (top) and payments (bottom) of

funded projects by experimental treatment (only rebate rule treat-

ments). ..................................120

4.6 Kernel density of pledges (top) and payments (bottom) of funded

projects by experimental treatment (only rebate rule treatments). . . 121

Chapter 1

General Introduction

“The interests of humanity may change, the present curiosities in science may cease,

and entirely different things may occupy the human mind in the future.”

John von Neumann

1.1 Economic Issues of the Digital Age

The Boston Computer Exchange is considered the world’s first e-commerce com-

pany and operated even before the widespread availability of the Internet. Just

like many of today’s online marketplaces, it virtually connected people and enabled

them to buy, sell, and trade. Although it was initially limited to the exchange

of used computers and regarded an oddity at the time, the Boston Computer Ex-

change was a progenitor for a new era of economic interactions. In this “economist’s

dream” intermediaries became obsolete, everyday items can be auctioned off, first-

and second-hand trading platforms emerged, and nowadays, instantaneous price

comparison became available between a plethora of different vendors offering simi-

lar or even identical goods, all-encompassed by the fact that local boundaries play

a limited or no role. Additionally, before making purchase decisions, buyers can

access expert reviews and customer opinions on products rather than relying solely

on the seller’s pitch.

These prospects of digitization seem exclusively beneficial at first glance, over-

coming many of the frictions of traditional markets, but even in this digital age,

economics is bound to be a science of trade-offs. While, in principle, anyone, any-

where, has an opportunity to interact and trade, we observe an increase in market

1.1. ECONOMIC ISSUES OF THE DIGITAL AGE

power, concentration, and newly arising monopolies. An infamous example is the

impact on (brick-and-mortar) bookstores, which started to wane when Amazon took

up its business. Emphasizing the fact that data is the “new oil”, four out of the five

largest companies of the world in terms of market capitalization are part of the “Big

Tech” firms (Alphabet, Amazon, Apple, and Microsoft; see Fool, 2023). Though

these firms offer unique services and serve different markets, they all have in com-

mon that they rely on vast amounts of data to maximize efficiency – rendering

competition without access to such information obsolete. In fact, the European

Union’s effort to protect personal data might even be considered detrimental as it

provides competitive advantages to firms outside its jurisdiction (Voss and Houser,

2019). However, there is a debate on the extent of optimal privacy rights, through-

out legal, psychological, political, and economic domains. While personalization

based on data is used for targeted discounts and advertisements, the enhancement

of services, and the customization and tailor-fitting of products, it is a mere small

step toward data breaches and infringement of privacy rights.

Although market concentration increased substantially as large companies grew

in a seemingly unstoppable fashion, there are also opportunities for the smallest

companies in the emerging creator economy. Crowdfunding is a substitute for tra-

ditional financing sources, not by massively out-scaling them but by decentralizing

and lowering the entry barriers. Independent vendors can offer products on plat-

forms (such as Amazon Marketplace, eBay, Etsy, et cetera) under entry costs that

are not even comparable with traditional flea markets.

Taken together, on the one hand, digital platforms can facilitate flourishing mar-

kets and even have the means to limit privacy concerns and protect privacy rights

by offering a secure digital infrastructure. On the other hand, platforms themselves

collect massive amounts of data, both on sellers and buyers. Thus, it is imperative to

analyze and regulate how platforms and firms work and operate under digitization

based on (inter alia) economic consequences. Whereas the opportunities to use dig-

ital tools for economic interactions are manifold, this dissertation focuses on a select

few. Explicitly, it addresses the following issues: personalized pricing, (online) pri-

vacy measures and (the shortcomings of) reward-based crowdfunding. To this end,

it draws from (neo-)classical economic models, such as models on spatial competi-

tion and threshold public good games and applies them to issues that have arisen

with digitization of economic interactions. All chapters incorporate an experimental

part, which tests, respectively goes beyond, the theoretical predictions.

This dissertation builds on influential contributions from different strands of

the economic literature. Chapters 2 and 3 build on a theoretical framework that

1.1. ECONOMIC ISSUES OF THE DIGITAL AGE

originated from Fudenberg and Tirole (2000), who, themselves, have progenitors

in form of works on price pre-commitment (Banerjee, 1987; Caminal and Matutes,

1990). Just as these older works, Fudenberg and Tirole (2000) featured a two-

period, linear city (Hotelling) model. However, they did not restrict themselves to

the case of price pre-commitment by departing from the notion that conditional

prices hinge on the availability of (analog) coupons – elevating the applicability

of these models toward the information age and into the 21st century. Chapter

2 scrutinizes the extent to which laboratory experiments are able to reproduce the

theoretical predictions of Fudenberg and Tirole (2000) and their successors. Chapter

3 enhances the model of Fudenberg and Tirole (2000) and the experimental approach

laid out in Chapter 2 by including privacy concerns and means for data protection.

Chapter 3 is mainly inspired by Acquisti (2008), who introduced a notion of identity

management that was later incorporated by Conitzer et al. (2012) as anonymizing

technologies, and by Acquisti and Grossklags (2005), who described that people

make irrational and contradicting privacy choices – a phenomenon that was later

coined “privacy paradox” by Norberg et al. (2007). While the origins of the provision

point mechanism can be traced back even further (e.g. Palfrey and Rosenthal, 1984),

Isaac et al. (1989) were probably the first to consider a quasi-continuous action space.

This is also a necessary requirement in the depiction of reward-based crowdfunding

in Chapter 4.

This dissertation contributes to the literature in multiple ways. In Chapter 2,

I examine under which conditions point predictions are met when implementing

behavior-based pricing models in laboratory experiments. Further, I explore how to

circumvent the impact of price distortions on efficiency measures when these con-

ditions are violated. In Chapter 3, we enrich the setting of Chapter 2 by allowing

consumers to endogenously determine their privacy setting. So far, endogenous pri-

vacy has been applied in monopolistic setups but not in the context of competitive

markets. We use methods from both theoretical industrial organization and behav-

ioral (and experimental) economics. While privacy concerns have been considered

separately in both fields, we are the first to create an integrated framework and an-

alyze this issue from both angles. This combination enriches both fields in different

ways. First, it introduces behavioral aspects to the model in an unenforced way, i.e.,

instead of modeling specific known behavioral biases, human behavior is introduced

naturally through participants in an experiment. Second, the framework allows us

to cleanly observe private, instead of personal, information so that the focus lies on

the strategic function of interacting with endogenously created private information.

In Chapter 4, we take a different approach by showing that experimental methods,

1.2. OUTLINE OF THE DISSERTATION

used to showcase the predictive power of Nash equilibria in Chapter 2, can also be

used to explore mechanisms when rational game-theoretic predictions cannot gen-

erate further insights. We consider reward-based crowdfunding – a threshold club

good game, which posits a coordination game in which it is explicitly hard to attain

Nash equilibrium results. We showcase that one cannot always count on (theoret-

ical) Nash equilibria when evaluating the efficacies of mechanisms, as differences

between them only manifest off the equilibrium paths.

1.2 Outline of the Dissertation

1.2.1 Chapter 2 – On Point Predictions in Behavior-based

Pricing Experiments

The first chapter of this dissertation presents findings from a single-authored pa-

per. I reassess the relevance and implications of theoretical point predictions for

behavior-based pricing experiments. While Brokesova et al. (2014a) and Mahmood

and Vulkan (2018) found that comparative static results hold in laboratory experi-

ments, they found that point predictions predominantly did not.

In this paper, I test whether these findings can be replicated under small alter-

ations of the experimental protocol over three treatments. In the first treatment

of my experiment, I introduce a new benchmark featuring simple uniform pricing,

i.e., the theoretical benchmark of Fudenberg and Tirole (2000). In the second treat-

ment, I replicate the behavior-based pricing case of Brokesova et al. (2014a), which

corresponds to the main short-term contract specification of Fudenberg and Tirole

(2000). Lastly, my third treatment is a follow-up experiment, in which I consider

the second period disjointed from the first period. For that, the second period is

preceded by a simulated first period based on the behavior of participants of the

second treatment.

I find that, under the right circumstances, point predictions are met under all

forms of pricing and in all stages of the competition. First of all, participants choose

prices in line with point predictions in the first treatment, i.e., under uniform pricing.

In contrast to Brokesova et al. (2014a), I observe first-period prices in line with the

theoretical prediction under behavior-based pricing. In line with Brokesova et al.

(2014a), I observe upward-shifted second-period prices under behavior-based pricing.

However, by disjoining the two periods, I show that reference dependence toward

first-period prices is accountable for the shift of second-period prices as there are no

price distortions in my follow-up experiment.

1.2. OUTLINE OF THE DISSERTATION

In a post hoc analysis, I show that considering myopic instead of strategic con-

sumers explains a downward shift of first-period prices and rationalizes the findings

of Brokesova et al. (2014a). Moreover, I show that transport costs are a robust wel-

fare measure that alleviates the impact of distorted prices, which affect price-based

welfare measures – such as seller profits and total customer costs.

The findings contribute to the literature in two ways. In a direct way, they

challenge the results of prior experimental studies on this topic. More generally, they

are relevant for the design and assessment of future multi-period pricing experiments.

1.2.2 Chapter 3 – We Value Your Privacy: Behavior-based

Pricing Under Endogenous Privacy

The second chapter presents joint work with Friederike Heiny and Tianchi Li. With

this theoretical and experimental study, we contribute to the ongoing issue of privacy

in markets by considering implications of the extension of open data directives to

the private sector. We show that consumers empowered by rights over their data

(e.g., due to the General Data Protection Regulation or the California Consumer

Privacy Act) would benefit from such a directive.

We endogenize the privacy choice of consumers in a framework based on the

duopolistic behavior-based pricing model of Fudenberg and Tirole (2000). Nat-

urally, endogenizing the privacy choice leads to two ways of distinction between

recognizable and anonymous customers. In the first way, which we consider an open

data policy, customers are recognizable by both firms. In the second way, which we

call an exclusive data policy, customers who bought from one firm revealing their in-

formation nevertheless remain anonymous to the other firm. We use this framework

to conduct a laboratory experiment as it allows for information to endogenously

arise and be used within the market interaction, distinguishing it from other works

on privacy that usually rely on personal information.

Under both data policies, we find a unique pure-strategy perfect Bayesian equi-

librium with contrasting privacy and distinct pricing choices. First, under the open

data policy, consumers reveal their data and firms employ price discrimination,

favoring consumer surplus. Second, under the exclusive data policy, consumers

anonymize and firms choose uniform prices, benefitting total welfare. Our experi-

mental findings are mixed. Sellers largely behave according to theory in the open

data treatment, while they only slowly adapt toward the predicted behavior in the

exclusive data treatment. Buyers share too little information in the open data treat-

ment but, initially, too much in the exclusive data treatment. However, when sellers

start adjusting pricing strategies, buyers adjust privacy choices as well.

1.2. OUTLINE OF THE DISSERTATION

We contribute to a large emerging body of literature on privacy and data protec-

tion in context of industrial organization by introducing it in the fundamental model

of behavior-based pricing. Further, since empirical evidence is extremely scarce, we

incorporate actual human behavior – instead of modeling irrational behavior – into

our framework through our experimental implementation.

1.2.3 Chapter 4 – Rebate Rules in Reward-based Crowdfund-

ing: Introducing the Bid-cap Rule

The last main chapter presents joint work with Fabian Gerstmeier and Yigit Oezce-

lik. We research ways to boost pledges and project success rates to enhance crowd-

funding platforms. Our focus is on incentivizing backers to pledge higher amounts

when first encountering a project that seeks to reach a funding goal by offering

rebates on their pledges when total pledges exceed the goal.

We develop a novel rebate rule called “bid-cap” rule. This rule sets an ex post cap

on eligible pledges, reducing any pledges exceeding it such that the funding goal is

exactly met. Additionally, we adapt the proportional rebate rule from the threshold

public goods literature and introduce both rules to a reward-based crowdfunding

framework. We derive theoretical properties and experimentally test both rules

against the customary all-or-nothing model.

All rules, i.e., the all-or-nothing model, proportional rebate rule, and bid-cap

rule, share the same efficient Nash equilibria. However, they differ with regards to

handling off-path over-pledging. While both rebate rules reduce the final payments

of backers such that the total pledges are equal to the funding goal, the bid-cap

rule does so by inducing a weakly lower variance in payments compared with the

proportional rebate rule. Experimentally, we find that both rebate rules increase

pledges and the project success rate significantly. While the theoretical property is

contingent on the fact that pledging behavior is sufficiently similar, we can in fact

confirm that the variance under the bid-cap rule is lower than under the proportional

rebate rule.

We contribute to the crowdfunding literature in particular by offering a new way

to increase pledges and specifically help projects borderline on reaching their goals

to succeed. Also, we contribute to the threshold public goods literature in general

by introducing a new rebate rule, which is intuitively understood and allows for a

simple implementation.

Chapter 2

On Point Predictions in Behavior-based Pricing

Experiments1

2.1 Introduction

Most papers on behavior-based pricing originated from Fudenberg and Tirole (2000,

henceforth F&T).2Most commonly, the models in these papers are characterized by

a two-period structure, where a continuum of consumers are served by two sellers at

uniform prices in the first period, and at differentiated prices in the second period.

The second-period prices are differentiated according to the first-period purchasing

decisions of consumers. Early successors of F&T include Chen and Pearcy (2010)

and Shin and Sudhir (2010), who studied the role of varying degrees of preference

dependence. As a second dimension, Chen and Pearcy (2010) evaluated the ability of

firms to commit to future prices, while Shin and Sudhir (2010) incorporate customer

heterogeneity.

Behavior-based pricing reemerged as a relevant topic over recent years with the

rise of digital markets and associated distribution channels. Recent academic contri-

butions cover behavior-based pricing and advertising (Shen and Miguel Villas-Boas,

2018; Esteves and Cerqueira, 2017), behavior-based pricing with vertical differen-

tiation (Garella et al., 2021; Umezawa, 2022), the observability of behavior-based

pricing (Li et al., 2020), and fairness concerns when behavior-based pricing prac-

1This chapter is the accepted manuscript published as: Tolksdorf, M. (2023). On Point Predic-

tions and Reference Dependence in Behavior-Based Pricing Experiments. Journal of Economics

and Behavioral Studies, 15(1(J), 1-14.

2See Fudenberg and Villas-Boas (2006a) and Esteves et al. (2009) for comprehensive literature

surveys of earlier contributions. Behavior-based pricing is also covered in Armstrong’s review of

recent developments in price discrimination (Armstrong, 2006a).

2.1. INTRODUCTION

tices are observed (Li and Jain, 2016). In response to recent developments in data

protection regulations, behavior-based pricing is studied when firms can personal-

ize prices and products (Capponi et al., 2021; Esteves, 2022; Laussel and Resende,

2022), the ability of firms to share customer information (De Nijs, 2017; Choe et al.,

2022, 2023), and consumer control over their data (Choe et al., 2018).

While there are empirical studies on behavior-based pricing (Asplund et al., 2008;

Cosguner et al., 2017), it might prove problematic to disentangle the aforementioned

factors and explicitly verify the mechanics of theoretical models. Laboratory exper-

iments allow fine control and adjustment of market features and grant first insights

into market dynamics. However, to our knowledge, only two experiments that ex-

plicitly featured behavior-based pricing have been conducted thus far.3Brokesova

et al. (2014a, henceforth BDP) implemented the model of Chen and Pearcy (2010)

experimentally by varying the ability of sellers to pre-commit to future prices and

the persistence of consumer preferences. Their first case directly corresponds to sim-

ple short-term contracts with independent preferences from F&T, while their second

case corresponds to poaching under short-term contracts (behavior-based pricing)

from F&T. By employing computerized buyers (while participants act as sellers),

their set-up closely resembles the structure of underlying theoretical models and is

suited to explicitly test point predictions. Mahmood and Vulkan (2018, henceforth

M&V) had participants play only the second period of a behavior-based pricing

market as sellers against computerized competitors, following a predetermined first

period. With their results, BDP and M&V supported the comparative static pre-

dictions of F&T and Chen and Pearcy (2010). However, their observed prices are

significantly larger than point predictions of the model. BDP’s observed profits

and customer costs and the profits in M&V are driven by skewed price levels and

predominantly do not reflect theoretical predictions.

The contribution of this paper is twofold. First, we explore why game-theoretic

point predictions of prices in behavior-based pricing models do not hold in labora-

tory experiments and whether there are circumstances under which they do. Second,

we show that transport costs are a suitable welfare measure whenever price predic-

tions do not hold (albeit comparative static results do). To this end, we derive the

subgame perfect prices of a parameterized version of F&T’s model. We then test the

predictions of the model by implementing a laboratory experiment where student

participants take the role of sellers and interact with computerized buyers.

3Mahmood (2014a) conducted an experiment motivated by Shin and Sudhir (2010) with par-

ticipants taking the roles of sellers and buyers. However, their experimental set-up is rather

reminiscent of a heterogenous goods Bertrand competition. Instead of a continuum of consumers

they consider two discrete locations. Due to this there are no pure strategy equilibria.

2.2. AN EXPERIMENT ON UNIFORM AND BEHAVIOR-BASED PRICING

In a benchmark uniform pricing treatment, we observe convergence toward price

predictions in both periods. This contrasts the first case of BDP, where partici-

pants chose lower second-period prices than were predicted. In our second treat-

ment, where behavior-based pricing is permitted, we observe that first-period prices

converge toward price predictions in contrast with BDP’s second case, while second-

period prices diverge from price predictions in line with BDP. In a follow-up ex-

periment, we only consider the second period using simulated first-period cutoffs.

This resembles the set-up of M&V, albeit allowing for a wider range of first-period

cutoffs and not featuring computerized sellers. In contrast to both M&V and our

second treatment, we do not observe a divergence of second-period prices. The most

puzzling discrepancy is the difference in first-period prices between the second case

of BDP and our behavior-based pricing treatment. Unlike BDP, we observe higher

prices and a peak in the distribution at the theoretical point prediction. The most

likely explanation for this difference is that BDP implemented myopic instead of

strategic consumers and participants used experimentation rather than deduction

in their pricing decisions. We show that assuming myopic consumers leads to a

theoretical prediction, which is in line with observed prices in BDP’s second case.

Welfare measures – such as customer costs and profits – are directly derived from

prices. When prices are volatile and prone to behavioral biases, these measures are

directly affected. We show that transport costs serve as a robust welfare measure,

which is independent of price levels but captures the impact of price dispersion and

poaching efforts by sellers.

2.2 An Experiment on Uniform and

Behavior-based Pricing

BDP analyzed behavior-based pricing while varying two dimensions: the ability

to price pre-commit and the extent of preference dependence. We step back from

this by contrasting whether sellers can employ behavior-based pricing or otherwise.

We do not consider price pre-commitment and only consider perfectly-dependent

preferences. Taken together, our set-up consists of a comparison of uniform and

behavior-based pricing, as detailed by F&T. We proceed by deriving subgame perfect

prices for both pricing regimes, which serve as predictions for our experiment. We

then introduce our experimental design and close by discussing the results.

2.2. AN EXPERIMENT ON UNIFORM AND BEHAVIOR-BASED PRICING

2.2.1 Theoretical Background

The market structure underlying this experiment closely follows F&T. Two sellers

i, j ∈ {A, B}with i=jare located at endpoints of a linear city model in the manner

of Hotelling with length ¯

θ. We assume that Ais located at 0and Bis located at

θ. Both sellers produce nondurable goods at constant marginal costs of cover two

periods n∈ {1,2}. Consumers are distributed uniformly over the interval [0,¯

θ]and

demand a maximum of one unit per period. Consumer valuation of the good is v,

and they incur transport costs which corresponds to the distance travelled. Thus,

a consumer located at ˆ

θreceives utility v−pA−ˆ

θwhen buying from seller A, and

v−pB−(¯

θ−ˆ

θ)when buying from seller B. Both sellers and consumers do not

discount the second period. Throughout, we assume vis sufficiently high to ensure

full market coverage.

Uniform pricing

In the first case, both sellers post a uniform price pn

iin each period n. After observing

prices pn

Aand pn

B, there is a consumer at θnwho is indifferent between buying from

Aor B. The location of the indifferent consumer is:

θn=pn

B−pn

A+¯

2.(2.1)

In each period, sellers face a static optimization problem:

Seller A: max

(pn

A−c)·θn,Seller B: max

(pn

B−c)·(¯

θ−θn).(2.2)

Solving the maximization problems, we find the following symmetric equilibrium

prices:

i=¯

θ+c. (2.3)

This aligns with the theoretical prediction for Case 1 “Independent preferences and

no price pre-commitment” of BDP, as every price is the one-shot Nash equilibrium

price.

Behavior-based pricing

In the second case, both sellers post a uniform price in period 1 (p1

Aand p1

B) and

employ behavior-based pricing period 2. Behavior-based pricing allows them to set

differentiated prices for old customers (pO

Aand pO

B) and new customers (pN

Aand pN

B),

dependent on the first-period purchasing decisions. A consumer who purchased from

2.2. AN EXPERIMENT ON UNIFORM AND BEHAVIOR-BASED PRICING

firm iin the first period is considered an old customer for firm iand a new customer

for firm j– and vice versa. We solve the game via backward induction. When

entering the second period, first-period prices p1

Aand p1

Bdetermine the location of

the indifferent consumer θ1, which sellers observe. Consumers on the interval [0, θ1]

bought from seller Ain period 1 and are denoted as A’s turf, while consumers on the

interval [θ1,¯

θ]bought from firm Band are denoted as B’s turf. Both sellers charge

the old customer price (pO

Aand pO

B) toward their own turf and the new customer

price (pN

Aand pN

B) toward the other seller’s turf. Given these prices, the locations

of the indifferent consumers on A’s and B’s turf are

θA=pN

B−pO

A+¯

2, θB=pO

B−pN

A+¯

2.(2.4)

In the second period, sellers solve the following optimization problems as functions

of θ1:

Seller A: max

A,pN

(pO

A−c)·θA+ (pN

A−c)·(θB−θ1),

Seller B: max

B,pN

(pO

B−c)·(¯

θ−θB)+(pN

B−c)·(θ1−θA).(2.5)

Using the first order conditions we can derive the optimal second-period prices as:

A=1

3(2θ1+¯

θ+ 3c), pN

A=1

3(3¯

θ−4θ1+ 3c),

B=1

3(3¯

θ−2θ1+ 3c), pN

B=1

3(4θ1−¯

θ+ 3c).

(2.6)

In the first period, forward-looking consumers can anticipate these pricing strategies.

The first-period cutoff θ1denotes the consumer who is indifferent between i) buying

from seller Ain the first period and switching to seller Bin the second period and

ii) buying from seller Bin the first period and switching to seller Ain the second

period. Following F&T, using pN

Aand pN

Bfrom (2.6), we find that the location of

the indifferent consumer is

θ1=3

8(p1

B−p1

A) + ¯

2.(2.7)

In the first period, forward-looking sellers face the following optimization problems:

Seller A: max

(p1

A−c)θ1+ (pO

A−c)θA+ (pN

A−c)(θB−θ1),

Seller B: max

(p1

B−c)(¯

θ−θ1)+(pO

B−c)(¯

θ−θB)+(pN

B−c)(θ1−θA).(2.8)

2.2. AN EXPERIMENT ON UNIFORM AND BEHAVIOR-BASED PRICING

We insert the expressions for θ1from (2.7) and for pO

A,pN

A,pO

Band pN

Bfrom (2.6),

and solve the resulting first order conditions for p1

Aand p1

Bto yield the symmetric

equilibrium prices as:

i=4

3¯

θ+c pO

i=2

3¯

θ+c pN

i=1

3¯

θ+c. (2.9)

This is equivalent to Case 2 “Constant preferences and no price pre-commitment” of

BDP.

2.2.2 Experimental Design

We implemented an experiment in line with BDP using two treatments, correspond-

ing to our two cases from Section 2.2.1. Similarly to BDP, we chose ¯

θ= 120 and

c= 50, so that results are easily comparable. As shown in Table 2.1, our predic-

tions for Treatment 1 “Uniform pricing” correspond to the predictions of Case 1 of

BDP, where the two afternoon prices (Price for loyal customers and Price for new

customers) of BDP are condensed into the singular Second-period price. Treatment

2 “Behavior-based pricing” is a replication of BDP’s Case 2.4

Treatment 1 2

Uniform

pricing

Behavior-based

pricing

Introduction price 170 210

Old customer price 130

New customer price 90

Second-period price 170

(a) Price predictions by treatment.

Case 1-Baseline 2

Buyer Preferences Independent Fixed

Price pre-commitment No No

Morning price 170 210

Price for loyal customers 170 130

Price for new customers 170 90

(b) Excerpt from Table 1 in BDP.

Table 2.1: Comparison of price predictions.

There are two minor differences between our experiment and that of BDP. First,

BDP framed the task as “ice-cream vendors on a beach”, whereas we kept the task

general, where the participants assume the role of a seller who is positioned at lo-

cation 0of a line, with another seller at the opposing end (at 120). As in BDP,

sellers learned that they were competing for computerized buyers who were uni-

formly distributed along the line. They were informed that buyers make decisions

considering prices and transport costs of both periods and seek to minimize their

total expenditures.5Second, in contrast to BDP who used matching groups of 4, we

4Our Introduction price corresponds to the Morning price, our Old customer price corresponds

to the Price for loyal customers and our New customer price corresponds to the Price for new

customers.

5Instructions and review questions were handed out in print and are available upon request.

2.2. AN EXPERIMENT ON UNIFORM AND BEHAVIOR-BASED PRICING

used the whole group of 20 participants in the first and 18 participants in the sec-

ond treatment as matching groups. As in BDP, participants played over 20 rounds,

where one round lasted for two periods and corresponded to the theoretical market.

Hence, in our experiment, participants were matched with each other slightly more

than once on average, decreasing reputation effects that could lead to tacit collusion.

The experiment was programmed and conducted with the experiment software

z-Tree (Fischbacher, 2007a). We conducted the experiment in the experimental

laboratory at TU Berlin in November 2016, with student participants drawn from the

WZB ORSEE pool (Greiner, 2015a), with experiments lasting around 90 minutes.

On average, participants earned e7.20 in the first treatment and e7.75 in the

second, in addition to a e5 show-up fee. Participants were aged 25 on average, with

around one third of the participants female. Around two thirds of all participants

were in currently enrolled in undergraduate studies, with industrial engineering and

natural sciences as the most common fields of study.

2.2.3 Results

Table 2.2 shows aggregated behavior between our two treatments on the left and

two cases of BDP on the right, where p-Values are based on Random Effects GLS

regressions on the difference between observed and predicted prices at the subject

level. While BDP observed no significant difference in their “Case 1” between both

second-period prices, they did find a difference between second-period prices and the

first-period price (see Afternoon price effect in Table 2.3b). We do not find a sig-

nificant difference between the corresponding introduction price and second-period

price in Treatment 1 (see Table 2.3a). Likewise, the distributions of introduction

and second-period prices are extremely similar in our Treatment 1 (as shown in

Figure 2.1a) in contrast to Case 1 of BDP (as shown in Figure 2.1b).

We observe a substantially larger average introduction price in our Treatment

2 compared with Case 2 of BDP. In addition, we observe a larger old customer

price, but a similar new customer price. As shown in the distribution of prices

in Figure 2.1a, we observe similar patterns for the introduction prices in both our

treatments, with a left-skewed distribution whose peak is close to the respective the-

oretical prediction. This is not the case in BDP, as seen in Figure 2.1b. Accordingly,

as shown in Table 2.3, we observe a much larger second-period price effect compared

with BDP’s corresponding Afternoon price effect, and a larger old customer price

effect compared with BDP’s corresponding Loyal customer price effect.

The introduction price in Treatment 2 is significantly larger than in Treatment

1 (see Table 2.4), confirming a treatment effect on the first-period price in line with

2.2. AN EXPERIMENT ON UNIFORM AND BEHAVIOR-BASED PRICING

Treatment 1 2

Uniform

pricing

Behavior-based

pricing

Introduction price

Observed mean 147.3 174.2

Model prediction 170 210

p-Value <0.001 <0.001

Old customer price

Observed mean 149.77

Model prediction 130

p-Value 0.013

New customer price

Observed mean 114.6

Model prediction 90

p-Value <0.001

Second-period price

Observed mean 141.4

Model prediction 170

p-Value <0.001

(a) Observed prices by treatment.

Case 1-Baseline 2

Buyer Preferences Independent Fixed

Price pre-commitment No No

Morning price

Observed mean 141.5 138.2

Model prediction 170 210

p-Value 0.002 <0.001

Price for loyal customers

Observed mean 119.7 129.2

Model prediction 170 130

p-Value <0.001 0.750

Price for new customers

Observed mean 116.5 114.1

Model prediction 170 90

p-Value <0.001 <0.001

(b) Excerpt from Table 2 in BDP.

Table 2.2: Comparison of observed prices.

Behavior-

Uniform based Follow-up

pricing pricing experiment

Second-period -5.890 -59.54∗∗∗

price effect (4.484) (5.393)

Old customer 35.13∗∗∗ 41.41∗∗∗

price effect (5.751) (4.371)

Constant 147.3∗∗∗ 174.2∗∗∗ 83.65∗∗∗

(3.795) (7.104) (3.685)

Observations 800 1080 796

Standard errors in parantheses. Estimation by OLS

regressions with standard errors clustered at the sub-

ject level. ∗∗∗ denotes significance at the 0.1% level.

(a) Analysis of prices within treatments.

Case 1-Baseline 2

Buyer Preferences Independent Fixed

Price pre-commitment No No

Afternoon price effect -25.028∗∗ -24.041∗∗∗

(7.227) (3.094)

Loyal customer price 3.250 15.022∗∗

effect (7.889) (3.857)

Constant 141.512∗∗∗ 138.172∗∗∗

(9.363) (1.306)

N of observations 960 960

Standard errors, clustered by matching group, are in

parantheses. ∗∗ and ∗∗∗ denote significance at the

1% and 0.1% level, respectively.

(b) Excerpt from Table 2 in BDP.

Table 2.3: Comparison of price effects.

the comparative static prediction of the model. This effect was absent in BDP. In

contrast to BDP, we see a larger rightwards shift for old customer prices and a wider

spread for new customer prices.

We find that prices converge toward their prediction in Treatment 1 by perform-

ing round-wise OLS regressions on the difference between observed and predicted

prices (see Table 2.5). By the last round, this difference is close to (and insignif-

icantly different from) zero for both the introduction price and the second-period

price. We observe a similar pattern for the introduction price in Treatment 2. How-

ever, we find a different pattern for second-period prices in Treatment 2. Both old

and new customer prices are not significantly different from their predictions in the

2.2. AN EXPERIMENT ON UNIFORM AND BEHAVIOR-BASED PRICING

100

Frequency

050 100 150 200 250

Introduction price

Treatment 1

Uniform pricing

100

Frequency

050 100 150 200 250

Introduction price

Treatment 2

Behavior-based pricing

100

Frequency

050 100 150 200 250

Second-period price

100

Frequency

050 100 150 200 250

Old customer price

100

Frequency

050 100 150 200 250

New customer price

(a) Distribution of prices by treatment. (b) Excerpt from Figure 2 in BDP.

Figure 2.1: Comparison of distribution of prices (solid lines represent predicted prices).

Introduction price Old customer price New customer price

Behavior-based pricing 26.85∗∗∗ 24.71∗∗ 30.94∗∗∗

(7.936) (8.281) (7.191)

Constant 147.3∗∗∗ 125.1∗∗∗ 83.69∗∗∗

(3.749) (2.672) (3.652)

Base case Uniform

pricing

Follow-up

experiment

Follow-up

experiment

Observations 760 758 758

Standard errors in parantheses. Estimation by random-effects GLS regressions with standard errors clustered at

the subject level. ∗∗ and ∗∗∗ denote significance at the 1% and 0.1% level, respectively.

Table 2.4: Analysis of prices between treatments.

beginning, but significantly larger than their predictions in the second half of the

experiment.6

In the spirit of backward induction, we first explore the apparent divergence

from predicted levels of second-period prices in behavior-based pricing experiments,

which is observed in both BDP and our experiment. Subsequently, we will show a

potential explanation for the disparity of first-period prices between BDP and our

experiment.

6Results in Table 2.5 use the subgame corrected predictions which are introduced in Sec-

tion 2.3.1 and are even stronger when not using the correction.

2.3. REFERENCE DEPENDENCE IMPACTS SECOND-PERIOD PRICES

Treatment 1

Uniform pricing

Treatment 2

Behavior-based pricing

Treatment 3

Follow-up experiment

Introduction

price

Second

period

price

Introduction

price

Old

customer

price

New

customer

price

Old

customer

price

New

customer

price

Round

1 -46.40∗∗∗ -51.60∗∗∗ -69.17∗∗∗ 0.444 7.444 -6.944 -10.56∗∗

(7.294) (7.399) (10.76) (10.59) (8.632) (7.839) (5.269)

2 -41.75∗∗∗ -52.30∗∗∗ -69.78∗∗∗ 2.833 14.97 1.500 -3.750

(7.820) (8.163) (10.40) (11.90) (11.98) (8.390) (7.626)

3 -39.65∗∗∗ -43.00∗∗∗ -60.39∗∗∗ 9.333 9.111 -14.85∗-13.55∗

(7.093) (7.408) (12.72) (14.25) (10.85) (7.953) (7.033)

4 -28.85∗∗∗ -40.90∗∗∗ -50.89∗∗∗ 15.22 11.58 0.400 -5.250

(7.071) (7.376) (11.11) (12.01) (8.244) (6.517) (10.09)

5 -27.75∗∗∗ -47.55∗∗∗ -53.06∗∗∗ 3.333 25.31∗-2.000 -5.700

(6.486) (8.890) (13.16) (13.83) (14.77) (8.470) (10.78)

6 -33.35∗∗∗ -40.50∗∗∗ -50.22∗∗∗ 6.778 17.78 -1.300 -3.250

(6.932) (6.771) (10.60) (11.94) (10.81) (6.641) (7.775)

7 -27.80∗∗∗ -38.15∗∗∗ -36.89∗∗∗ 15.50 26.47∗∗∗ -5.550 -5.675

(6.296) (8.601) (11.05) (11.40) (9.035) (7.881) (8.784)

8 -28.65∗∗∗ -40.10∗∗∗ -40.56∗∗∗ 17.83 20.11 -3 -6.800

(7.536) (9.523) (10.72) (11.16) (13.32) (5.468) (4.351)

9 -28.80∗∗∗ -29.90∗∗∗ -47.17∗∗∗ 2.444 12.97 -8.000 -6.900

(7.019) (8.034) (11.54) (10.91) (9.963) (5.462) (8.724)

10 -20.40∗∗ -23.10∗∗ -39.22∗∗∗ 14.11 32.78∗∗∗ 1.300 -5.450

(8.451) (10.73) (7.870) (8.999) (10.80) (6.227) (5.879)

11 -18.40∗∗ -24∗∗ -27.39∗∗∗ 17.33 36.00∗∗∗ -7.750 -7.525

(9.240) (11.33) (7.903) (12.82) (11.17) (7.772) (9.521)

12 -19.15∗∗∗ -19.15∗∗∗ -18.39∗∗ 31.61∗∗∗ 45.72∗∗∗ -7.800∗-10

(6.986) (7.304) (7.867) (11.82) (12.40) (4.690) (8.398)

13 -16.85∗∗ -14.85∗∗ -27.56∗∗∗ 28.61∗∗∗ 22.78∗∗ -8.150 -4.750

(6.944) (7.495) (9.107) (9.617) (11.18) (5.697) (10.49)

14 -14.90∗∗ -19.60∗∗ -31.56∗∗ 15.78 21.86∗-10.75 -6.650

(7.376) (7.917) (12.19) (14.08) (12.56) (7.283) (6.883)

15 -11.35∗-21.75∗∗∗ -21∗∗ 17.33 24.36∗∗ -10.40∗-8.000

(6.140) (7.465) (9.986) (11.94) (11.01) (5.540) (5.410)

16 -16.20∗∗ -20.40∗∗ -18.39∗∗∗ 28.17∗∗∗ 26∗∗ -19.05∗∗∗ -13.90∗∗

(7.649) (8.408) (7.001) (9.779) (11.44) (6.669) (6.912)

17 -13.60∗∗ -13.60∗-21.89∗∗ 20.11∗22.00∗∗ -8.150 -7.650

(6.076) (7.237) (9.465) (11.42) (10.77) (5.430) (6.580)

18 -6.850 -11.15 -17.44∗∗ 31.44∗∗∗ 28.42∗∗∗ -1.700 2.200

(4.343) (6.787) (7.375) (10.51) (10.96) (9.692) (12.20)

19 -7.000∗-11.30∗∗ -11.94 35.94∗∗∗ 38.56∗∗∗ -7.750 -8.450

(3.669) (5.590) (8.432) (12.01) (11.64) (5.786) (5.496)

20 -5.950 -8.550 -3.667 30.17∗∗ 22.94∗∗ -9.500 -11

(4.529) (5.196) (10.68) (12.98) (11.23) (5.784) (7.498)

Standard errors in parentheses. Estimation by round-wise OLS regressions. Coefficients are the difference between

observed and predicted prices. ∗,∗∗ and ∗∗∗ denote significance at the 10%, 5% and 1% level, respectively.

Table 2.5: Regressions on difference between observed and predicted prices per round and treat-

ment.

2.3 Reference Dependence Impacts

Second-Period Prices

In the below section, we explore why second-period prices seemingly diverge from

their predictions in Treatment 2 by limiting our attention to the second period.

We begin by showing that theoretical subgame predictions for second-period prices

increase whenever the cutoff is insufficiently centered, but that this increase does not

2.3. REFERENCE DEPENDENCE IMPACTS SECOND-PERIOD PRICES

account for observed second-period prices in both BDP and our experiments. We

then present the design and results of a follow-up experiment where we simulate the

first-period cutoffs based on our previous findings. Using this, we keep the model

predictions constant, but eliminate the first-period price as a potential reference

point for participants when choosing second-period prices.

2.3.1 Theoretical Preamble

In the following section we attempt to rule out asymmetric market shares as the

sole driver for the higher than predicted second-period prices in our Treatment 2

and Case 2 of BDP. The equilibrium in (2.9) is symmetric and implies θ1=¯

θ/2. In

Treatment 2, we observe first-period cutoffs between the full range of 0and ¯

θ= 120,

while only 3.89% of the observed cutoffs are exactly ¯

θ/2 = 60. Hence, we need to

check whether first-period cutoffs of θ1=¯

θ/2affect second-period prices.

Let us fully specify the optimal second-period prices from (2.6) for both firms:

A=⎧

⎪

⎨

⎪

⎩

3(2θ1+¯

θ+ 3c)if θ1≥1

4¯

θ−2θ1+cif θ1<1

4¯

, pN

A=⎧

⎪

⎨

⎪

⎩

3(3¯

θ−4θ1+ 3c)if θ1≤3

4¯

cif θ1>3

4¯

B=⎧

⎪

⎨

⎪

⎩

3(3¯

θ−2θ1+ 3c)if θ1≤3

4¯

2θ1−¯

θ+cif θ1>3

4¯

, pN

B=⎧

⎪

⎨

⎪

⎩

3(4θ1−¯

θ+ 3c)if θ1≥1

4¯

cif θ1<1

4¯

(2.10)

Now, we denote the average prices for old and new customers respectively as ¯pO=

(pO

A+pO

B)/2and ¯pN= (pN

A+pN

B)/2dependent on θ1and get:

(¯pO,¯pN)=

⎧

⎪

⎨

⎪

⎩

(¯

θ−4

3θ1+c, ¯

2−2

3θ1+c)if θ1<1

4¯

3¯

θ+c, ¯

3+c)if 1

4¯

θ≤θ1≤3

4¯

3θ1−¯

3+c, 2

3θ1−¯

6+c)if θ1>3

4¯

.(2.11)

A change in the first-period cutoff does not affect the average old and new customer

prices while θ1∈[¯

θ/4,3·¯

θ/4]. When correcting the model predictions for Treatment

2, according to (2.10) we would expect an average old customer price of 132.55

instead of 130, and an average new customer price of 91.275 instead of 90.7The

7First-period cutoffs were not sufficiently centered in 1/6of our observations and caused a

2.3. REFERENCE DEPENDENCE IMPACTS SECOND-PERIOD PRICES

results presented in Table 2.5 are created under these corrected model predictions.

Thus, we can rule out asymmetric first-period market shares as a driver for higher

second-period prices as the increase in predicted prices is not substantial and does

not explain observed higher prices.

2.3.2 Experimental Follow-up

We conducted an additional Treatment 3 “Follow-up experiment” in which we omit-

ted the first period of Treatment 2. We provided participants with the required

information – the first-period cutoff – without providing them the theoretically un-

necessary information on first-period prices. Similar to the previous experiment,

participants took the role of sellers and posted prices for “near” and “far” customers.

The near customers correspond to the old customers, while far customers corre-

spond to the new customers in Treatment 2.8Participants were presented with

randomly simulated first-period cutoffs and learned that these were derived from

earlier experiments.

Using a Q-Q plot, Shapiro-Wilk tests, and Shapiro-Francia tests, we confirmed

that the first-period cutoffs follow normal distributions – both overall and for each

individual period. However, around 60% of the observations were multiples of 3.75,

which occurs whenever the difference of chosen prices is a multiple of 10. To account

for this, we drew the according share of cutoffs from a truncated normal distribution

of multiples of 3.75, and the rest from a normal distribution of multiples of 0.375.9

Furthermore, we accounted for the fact that 3.75 is a multiple of 0.375 when speci-

fying the respective shares. We did this by first drawing from a uniform distribution

on the interval [0,1] to determine from which of the two normal distributions to

draw given a critical value. The critical value is derived from the observed share of

cutoffs which are multiples of 3.75 named s10, and those that are not s−10 by solving

the following system of equations:

s10 =scrit

10 +scrit

−10

10 ,

s−10 =9

10scrit

−10,

s−10 = 1 −s10.

(2.12)

change in the predicted average prices.

8For the remainder of this paper, we will refer to the customers in Treatment 3 as “old” and

“new” customers.

9The most common integer step of differences between two prices is 3

8·10 = 3.75. The smallest

integer step of differences between two prices is 3

8·1=0.375.

2.3. REFERENCE DEPENDENCE IMPACTS SECOND-PERIOD PRICES

For example, if for a given round the first-period price difference was a multiple of

10 in 6 out of 10 markets, i.e., s10 = 0.6, we would find the critical cutoff value

scrit

10 = 0.55. To keep the draws as close to the original observations as possible and

avoid situations for the participants that did not occur in the original experiment,

we fixed the mean at 60. However, we varied the lower bound, upper bound, stan-

dard deviation, and the critical value scrit

10 for each round according to the original

experimental values of the respective round. Truncated normal distributions are

achieved by redrawing an observation when it is either below the lower bound or

above the upper bound. Given that the lower bounds (upper bounds) are well below

(above) the mean at a considerably low standard deviation, this approach is highly

efficient (see Robert, 1995; Chopin, 2011).

The follow-up experiment was conducted in October 2018 in the experimental

laboratory at TU Berlin. As with the first two treatments, student participants were

drawn from the WZB ORSEE pool and shared similar demographic characteristics

(age, gender, and field of study). The experiment was slightly shorter in duration (at

60 minutes) as no first period was played. 20 participants earned e6.24 on average,

in addition to a e5 show-up fee. The exchange rate was increased so that the total

payment remained comparable to the first two treatments.

2.3.3 Findings

Comparisons of aggregate prices in Table 2.6 and the distribution of prices in Fig-

ure 2.2 reveal that second-period prices are not significantly different from their

model prediction, at a 5% significance level in Treatment 3.10 Both second-period

prices are significantly lower in Treatment 3 compared with Treatment 2 (see Ta-

ble 2.4). These findings contrast with those of M&V, who observed that prices are

significantly higher than model predictions in a similar experiment – also limited to

the second period.

For the subsequent discussion, we correct model predictions by calculating second-

period predictions following (2.10). However, we only find marginal impact of these

corrections with an average predicted old customer price of 131.53, and an average

predicted new customer price of 90.76.

We have shown that, in Treatment 2, second-period prices increase along with

the introduction price. In Treatment 3 (where the first period is absent) there is

no considerable change in prices over rounds, as shown by the round-wise OLS

regressions in Table 2.5. We only observe two rounds in which both the old and new

10Again, p-Values are based on random-effects GLS regressions on the difference between ob-

served and predicted prices at the individual level.

2.4. MYOPIC CONSUMERS INDUCE LOWER FIRST-PERIOD PRICES

Treatment 2 3

Behavior-based

pricing

Follow-up

experiment

Old customer price

Observed mean 149.77 125.06

Model prediction 130 130

p-Value 0.013 0.068

New customer price

Observed mean 114.6 83.65

Model prediction 90 90

p-Value <0.001 0.088

Table 2.6: Observed prices (follow-up).

100

Frequency

050 100 150 200 250

Old customer price

Treatment 2

Behavior-based pricing

100

Frequency

050 100 150 200 250

Old customer price

Treatment 3

Follow-up experiment

100

Frequency

050 100 150 200 250

New customer price

100

Frequency

050 100 150 200 250

New customer price

Figure 2.2: Distribution of prices (follow-up).

customer prices are significantly different from their predictions, and three instances

where one of the two prices is significantly different from the prediction.11

We still observe a significant old customer price effect with a similar effect size

(as in the behavior-based pricing treatment), as shown in Table 2.3a. This indicates

that the presence of the first period does impact overall price levels in the second

period but does not affect poaching efforts.

2.4 Myopic Consumers Induce Lower

First-period Prices

While we have shown that the upwards price shift in the second period is driven by

the availability of the first-period prices, there are remarkable differences between

the chosen first-period prices in Case 2 of BDP compared with the second treatment

in our experiment. In the following discussion, we conjecture that this may have

been driven by a faulty fraction in the computation of the first-period cutoff in the

code of BDP’s program. We argue that this represents a case of “Behavior-based

pricing with myopic consumers”. To support this argument, we first derive the

subgame perfect prices of a myopic consumer variation of F&T’s model. We then

show that the result is a better prediction of BDP’s observations.

Behavior-based pricing with myopic consumers

Whether consumers are naïve or strategic only alters their actions in the first period.

Hence, we can readily skip the analysis of the second period as it is identical to the

case of behavior-based pricing in section 2.2.1. Due to the naivety of consumers, the

11Four out of the seven significant differences only hold at a complaisant significance level of

90%.

2.4. MYOPIC CONSUMERS INDUCE LOWER FIRST-PERIOD PRICES

location of the indifferent consumer in period one θ′

1is akin to the location of the

indifferent consumer under uniform pricing, i.e.,

θ′

1=p1

B−p1

A+¯

2.(2.13)

The maximization problems of firms are like (2.8) with θ′

1inserted instead of θ1:

Seller A: max

(p1

A−c)θ′

1+ (pO

A−c)θA+ (pN

A−c)(θB−θ′

1),

Seller B: max

(p1

B−c)(¯

θ−θ′

1)+(pO

B−c)(¯

θ−θB)+(pN

B−c)(θ′

1−θA).(2.14)

Solving the maximization problems for p1

Aand p1

Bwith consideration of θ′

1from

(2.13) and optimal second period prices from (2.6), where we replace θ1by θ′

yields:

i=¯

θ+c. (2.15)

This result is identical to the result under uniform pricing in (2.3).12

Case 1 of BDP and the case of “Behavior-based pricing with myopic consumer”

both share the term (p1

B−p1

A+¯

θ)/2as a first-period cutoff. Case 2 of BDP and

our behavior-based pricing case are different in this term, as shown in (2.7) where

the difference in prices p1

B−p1

Ais multiplied by 3/8instead of 1/2. For Treatment

1 and Treatment 2 in our experiment (as well as for Case 1 of BDP), we observe

a peak in the price distribution close to the model prediction whenever a uniform

price is chosen in the first period (see Figure 2.1). This only fails for Case 2 of BDP,

where prices are similar to their Case 1 and our Treatment 1, with a peak in the

price distribution at a similar point – just below 170. However, this would be in line

with the price prediction in (2.15).

While this does not fit the instructions of BDP – according to which consumers

are strategic in their first-period decision – it is a surprising testament to how power-

ful price predictions are in this model. It should be noted that BDP’s instructions are

somewhat vague concerning buyer behavior in the first period. Buyers are described

as minimizing their total expenditures with their first-period decision (considering

their location and the current prices) while anticipating optimally chosen prices in

the second period. On the other hand, second-period behavior is described explic-

itly, covering precise calculations of the location of the indifferent consumer and the

resulting cutoff. It may not be immediately apparent to an uninformed participant

that the strategic decision of a consumer in the first period involves a lowered will-

12The uniform pricing benchmark is identical for myopic and strategic consumers, due to the

independence of the periods.

2.5. TRANSPORT COSTS AS A ROBUST WELFARE MEASURE

ingness to buy from a far seller. Rather than relying on instructions, participants

appeared to have experimented over the course of the experiment to optimize their

pricing decisions.

2.5 Transport Costs as a Robust Welfare Measure

As discussed previously, chosen prices are prone to distortions. Therefore, we hold

reasonable doubt regarding the reliability of consumer costs and profit as welfare

measures, as used by BDP. Both measures are easily shifted by price levels and mask

the efficiency of the market. Instead, we propose to measure total welfare directly by

means of transport costs. While this is not necessarily the preferred welfare measure

in terms of policy recommendations, it is superior when assessing the efficiency of an

experimental market. This is sensitive to comparative static implications (such as

poaching and efficiency losses due to price dispersion), but insensitive to distorted

price levels. Under uniform pricing the transport costs are:

T=∫θ1

θ dθ +∫¯

θ1

(¯

θ−θ)dθ +∫θ2

θ dθ +∫¯

θ2

(¯

θ−θ)dθ. (2.16)

Transport costs under behavior-based pricing are:

T=∫θ1

θ dθ+∫¯

θ1

(¯

θ−θ)dθ+∫θA

θ dθ+∫θ1

θA

(¯

θ−θ)+∫θB

θ1

θ dθ+∫¯

θB

(¯

θ−θ)dθ. (2.17)

It is noteworthy that gains are independent of consumer purchasing decisions when

the market is fully covered. Hence, it is sufficient to consider losses in the form of

transport costs in (2.16) and (2.17) to evaluate welfare effects.

In Table 2.7, we show how profits for sellers and total costs for consumers were

lower under uniform pricing compared with behavior-based pricing in the first pe-

riod, in contrast to BDP who found no effect. This finding is driven by higher

introduction prices in our Treatment 2 (compared with Case 2 of BDP). However,

transport costs were not significantly different in the first period between both treat-

ments. The difference in total costs can be entirely explained by the difference in

prices paid (i.e., product costs). Second-period profits and total costs are larger

in Treatment 1 compared with Treatment 2 – oppositional to the findings of BDP.

Transport costs are significantly different between the uniform pricing and behavior-

based pricing treatments in the second period. In contrast, there are no differences

in transport costs between the follow-up experiment and the behavior-based pricing

treatment, while profits and total costs were significantly smaller in the follow-up

2.5. TRANSPORT COSTS AS A ROBUST WELFARE MEASURE

experiment compared with the behavior-based pricing treatment. This is a direct

consequence of the lower prices chosen by participants.

Seller’s Customers’ Seller’s Customers’

profit total

costs

transport

costs

profit total

costs

transport

costs

Treatment 1 -1374.7∗∗∗ -2820.8∗∗∗ -71.48 572.2∗∗ 386.1 -758.2∗∗∗

(158.5) (366.8) (73.40) (174.0) (405.9) (90.28)

Treatment 3 -1396.2∗∗∗ -2821.9∗∗∗ -29.46

(151.6) (342.5) (95.54)

Constant 5150.0∗∗∗ 20339.9∗∗∗ 4039.9∗∗∗ 3844.9∗∗∗ 18344.3∗∗∗ 4654.5∗∗∗

(324.6) (876.5) (114.7) (243.0) (627.1) (132.6)

Base case Treatment 2 Treatment 2 Treatment 2 Treatment 2 Treatment 2 Treatment 2

Considered period First First First Second Second Second

Observations 760 380 380 1158 579 579

Standard errors in parentheses. Estimation by OLS regressions with round fixed effects. Analysis is done on

individual level for sellers and on market level for customers. Treatment 1 - Uniform pricing, Treatment 2 -

Behavior-based pricing, Treatment 3 - Follow-up experiment. ** and *** denote significance at the 1% and 0.1%

level, respectively.

Table 2.7: Treatment effects on welfare measures in the first and second period.

We show the effect of disjoining the decision process in Table 2.8. There, we

calculated mean profits, mean total costs and mean transport costs for three cases.

The first and second case correspond to the first and second treatment. In the third

case we hypothetically combine the second-period findings of the follow-up exper-

iment with the results of the first period of the behavior-based pricing treatment.

Both mean profits and total costs are lower in the combined case compared with

the uniform pricing treatment, whereas they were originally larger in the behavior-

based pricing treatment (compared with the uniform pricing treatment). In contrast,

the sign and the magnitude of the differences in transport costs between both the

behavior-based pricing and the uniform pricing treatment and the combined case

and the uniform pricing treatment remain similar. This shows that price-based mea-

sures (profits and total costs) are volatile and can mask efficiency. Transport costs

are independent of prices and reflect the efficiency of the market without distortion.

Considered

treatment in

First period Uniform pricing Behavior-based pricing Behavior-based pricing

+ + +

Second period Uniform pricing Behavior-based pricing Follow-up experiment

Sum of mean

profits 10485.44 11287.95 9895.11

total costs 20498.92 21716.29 20308.95

transport costs 4013.48 4428.334 4413.841

Table 2.8: Sum of mean profits, total costs and transport costs between cases.

2.6. CONCLUSION

2.6 Conclusion

We designed an experiment using the theoretical basis provided by F&T and a

previous experiment by BDP. In contrast to BDP, we can confirm the positive

first-period price effect of behavior-based pricing over uniform pricing, validating an

additional comparative static result from F&T’s model. We find that, in the case of

behavior-based pricing, second-period prices are driven upwards when participants

play the first period themselves – but not when both periods are disjointed and

played by different participants. This also contrasts with the findings of M&V, who

observed significantly larger-than-predicted prices when participants play a disjoint

second period against computerized competitors.

While our study does not require direct policy recommendations, it questions the

circumstances that necessitate policy recommendations drawn from experimental

studies, and to what extent. Separating the decisions of the first and second period

reveals a particular volatility within the chosen strategies. Going forward, this

insight can be helpful in the fundamental design of experiments. For multi-period

experiments, separating the individual stages may be necessary to reveal conclusively

whether participants play according to predictions. Furthermore, when volatility is

anticipated, welfare measures should be chosen carefully. In the case of behavior-

based pricing experiments, we have shown that transport costs are a welfare measure

that is robust to confounding factors.

Some pertinent questions remain and could be investigated further in future

research. It remains unclear precisely how first-period prices drive second-period

prices up in the behavior-based pricing cases in BDP and our experiment. It is pos-

sible that prices are interpreted as signals and change beliefs toward second-period

behavior. Another possibility is that first-period prices have an anchoring effect; this

could be resolved by showing either first-period prices of past experiments (along

with the first-period cutoffs) or irrelevant numbers of the same magnitude (that

serve as anchors for participants) in a follow-up experiment. Moreover, we cannot

explain why participants in BDP’s Case 1 chose lower prices in the second period.

They may not have understood that, because consumers have independent prefer-

ences, the two resulting markets can be treated as two separate markets. Again, this

question could likely be answered by separating the confounding factors and con-

ducting an experiment in which participants are confronted with two independent

markets in the second period.

2.7. TRANSLATED INSTRUCTIONS AND REVIEW QUESTIONS

2.7 Translated Instructions and Review Questions

[Text in brackets was not observed by the subjects.]

Instructions

Welcome to the experiment! From now on, please do not talk to the other participants in

the experiment.

Below are the instructions for the experiment. They are identical for all participants.

In the experiment you will make simple decisions on the computer. All decisions remain

anonymous. This means that you do not learn the identity of the other participants and

no participant learns your identity. Your payout depends on your decisions and the deci-

sions of the other participants. All monetary information within the experiment is given in

ECU (Experimental Currency Unit). Please read the instructions carefully. If you don’t

understand something, please show it with a hand signal. We will then come to you and

answer your questions privately.

What am I doing in the experiment?

[Treatment 1 / Treatment 2]

You are a seller of a good. You are in competition with another seller who is selling the

same good. You and the other seller are in a town at either end of a 120 meter street

for 2 periods. All potential buyers of your good are between you and the other seller and

are evenly and continuously spread across the street. There is one buyer per one meter of

street, making for 120 buyers in total. Each buyer wants to buy exactly one good in the

first and in the second period. At the beginning of a period, you and the other seller set

the prices of the goods at the same time. In addition to the price of a good, a buyer incurs

one ECU for every one meter distance to a seller.

[Treatment 3]

You are a seller of a good. You are in competition with another seller who is selling the

same good. You and the other seller are in a town at either end of a 120 meter street.

All potential buyers of your good are between you and the other seller and are evenly and

continuously spread across the street. There is one buyer per one meter of street, making

for 120 buyers in total. Each buyer wants to buy exactly one good at a time. You and

the other seller set the prices of the goods at the same time. In addition to the price of a

good, a buyer incurs one ECU for every one meter distance to a seller.

[End Treatments]

2.7. TRANSLATED INSTRUCTIONS AND REVIEW QUESTIONS

Costs to Customer = Price + Distance to Seller

your Location other Seller

0 120

Distance = XDistance = 120 −X

Suppose you set a price of 140 ECU and the other seller sets a price of 160 ECU. A buyer

at location X = 50 would incur costs of 190 ECU to buy from you. Of this, 140 ECU are

due to the price of the good and 50 ECU are due to distance. The same buyer would incur

costs of 230 ECU to buy from the other seller. Of this, 160 ECU are due to the price and

70 ECU are due to distance.

[Treatment 1 / Treatment 2]

At the beginning of the first period, you and the other seller simultaneously set a price for

the first period. You then find out the price that the other seller set and how many buyers

bought from you (your customers in period 1 / your period 1-customers). This ends the

first period and the second period begins.

[Treatment 1]

At the beginning of the second period, you and the other seller set a price for the

second period. You will then find out the price that the other seller set and how many

buyers bought from you (your customers in period 2).

[Treatment 2]

At the beginning of the second period you set two prices, one price for your period

1-customers and one price for the other seller’s period 1-customers. The other seller also

sets prices for your and their period 1-customers. You will then find out the prices that

the other seller has set, how many customers have bought from you again (from now on

old customers) and how many of the other seller’s period 1-customers have bought from

you (from now on new customers).

[Treatment 3]

You are in town for two periods, and you only become active in the second period. In

the first period, the buyers are divided into your adjacent customers and the other seller’s

adjacent customers. This ends the first period and the second period begins.

At the beginning of the second period, you set two prices, one price for your adjacent

customers and one price for the other seller’s adjacent customers. The other seller also

sets prices for your and their adjacent customers. You will then find out the prices the

other seller set and how many of their adjacent customers bought from you (henceforth

your near customers) and how many of the other seller’s adjacent customers bought from

you (henceforth your far customers).

[End Treatments]

2.7. TRANSLATED INSTRUCTIONS AND REVIEW QUESTIONS

Each unit of the good you sell costs you 50 ECU. The other seller also has costs of 50

ECU per unit. Your profit is determined from the revenue of your sold units, i.e. the price

minus the costs, as well as the number sold and is added up over both periods. Losses are

offset against your profits and therefore have a negative effect.

[Treatment 1]

Profit in Period 1 = (Price in Period 1 −Costs)·Customers in Period 1

Profit in Period 2 = (Price in Period 2 −Costs)·Customers in Period 2

Profit = Profit in Period 1 +Profit in Period 2

[Treatment 2]

Profit in Period 1 = (Price in Period 1 −Costs)·Customers in Period 1

Profit in Period 2 = (Price for old Customers −Costs)·old Customers

+ (Price for new Customers −Costs)·new Customers

Profit = Profit in Period 1 +Profit in Period 2

[Treatment 3]

Profit = (Price for near Customers −Costs)·near Customers

+ (Price for far Customers −Costs)·far Customers

[End Treatments]

The two periods form a round. You sell your goods over 20 rounds. In each new round,

a different randomly selected participant in the experiment takes on the role of the other

seller, and you find yourself in a new city, with new buyers.

I am a seller, who are the buyers?

[Treatment 1 / Treatment 2]

Buyers are automated by the computer. All buyers remain in the same place for the course

of the two periods, i.e. one round. In the first period, buyers consider prices, their location

and their expectations for the second period and want to minimize their overall costs.

That is, buyers anticipate that both sellers will choose optimal prices in the second period,

taking into account the results of the first period. There is a cutoff S1on the road at the

end of the first period. All buyers between you and the cutoff S1buy from you (these are

your customers in period 1 / these are your period-1 customers), while all buyers between

S1and the other seller buy from the other seller.

2.7. TRANSLATED INSTRUCTIONS AND REVIEW QUESTIONS

[Treatment 3]

Buyers are automated by the computer. All buyers remain in the same place for the course

of the two periods, i.e. one round. There is a cutoff S1on the road at the end of the first

period. All buyers between you and the cutoff S1are said to be your adjacent customers,

while all buyers between S1 and the other seller are said to be the other seller’s adjacent

customers. The cutoff S1cannot be influenced by you and corresponds to observations

from a past experiment.

[Treatment 1]

your Location other Seller

0 120

your Customers

in Period 1

your Customers

in Period 2

In the second period, the buyers make their decision based on the costs that are most

favorable to them. So the buyers compare between your price and distance to you and the

other seller’s price and distance to the other seller. There will be a cutoff S2. All buy-

ers between you and S2will buy from you (your customers in period 2), while all buyers

between S2and the other seller will buy from the other seller. Calculating the cutoff in

period 2:

your Price in

Period 2 +S2=Price of Other

in Period 2 + (120 −S2)

⇐⇒ S2=

Price of Other

in Period 2 −your Price in

Period 2 + 120

[Treatment 2]

your Location other Seller

0 120

your Customers

in Period 1

your old Customers

in Period 2

Sold

your new Customers

in Period 2

Snew

In the second period, buyers make their decision based on the costs that are most favorable to

them. Your period 1-customers compare your price for your period 1-customers and the price for

your period 1-customers of the other seller, taking into account their location. All buyers among

your period 1-customers between you and cutoff Sold

2buy from you (these are your old customers).

The rest of your period 1-customers, between cutoffs Sold

2and S1, buy from the other seller at his

price for your period 1-customers.

2.7. TRANSLATED INSTRUCTIONS AND REVIEW QUESTIONS

The same is true on the other seller’s period 1-customers segment. There, the buyers com-

pare between your price for the other seller’s period 1-customers and their price for their period

1-customers, taking into account their location. All buyers among the other seller’s period 1-

customers between cutoffs S1and Snew

2buy from you (these are your new customers). The re-

maining buyers in this segment buy from the other seller. The calculation of the cutoffs in period 2:

your Price for your

Period 1-Customers +Salt

2=Price of Other for your

Period 1-Customers + (120 −Salt

⇐⇒ Sold

Price of Other for your

Period 1-Customers −your Price for your

Period 1-Customers + 120

your Price for Period 1-

Customers of Other +Sneu

2=Price of Other for

their Period 1-Customers + (120 −Sneu

⇐⇒ Snew

Price of Other for

their Period 1-Customers −your Price for Period 1-

Customers of Other + 120

[Treatment 3]

your Location other Seller

0 120

your adjacent Customers

in Period 1

your near Customers

in Period 2

Snear

your far Customers

in Period 2

Sfar

In the second period, buyers make their decision based on the costs that are most favorable to them.

Your adjacent customers compare your price for your adjacent customers and the price for your

adjacent customers of the other seller, taking into account their location. All buyers among your

adjacent customers between you and cutoff Sold

2buy from you (these are your near customers).

The rest of your adjacent customers, between cutoffs Snear

2and S1, buy from the other seller at

their price for your adjacent customers.

The same is true on the other seller’s period 1-customers segment. There, the buyers compare

between your price for the other seller’s adjacent customers and their price for their adjacent cus-

tomers, taking into account their location. All buyers among the other seller’s adjacent customers

between cutoffs S1and Sfar

2buy from you (these are your far customers). The remaining buyers

in this segment buy from the other seller. The calculation of the cutoffs in period 2:

your Price for your

adjacent Customers +Snear

2=Price of Other for your

adjacent Customers + (120 −Sbear

⇐⇒ Snear

Price of Other for your

adjacent Customers −your Price for your

adjacent Customers + 120

your Price for adjacent

Customers of Other +Sfar

2=Price of Other for

their adjacent Customers + (120 −Sfar

2.7. TRANSLATED INSTRUCTIONS AND REVIEW QUESTIONS

⇐⇒ Sfar

Price of Other for

their adjacent Customers −your Price for adjacent

Customers of Other + 120

[End Treatments]

Example

[Treatment 1]

Suppose you set a price of 100 ECU in period 1 and all buyers up to cutoff S1at point 70 buy

from you after comparing the price of the other seller. So you have 70 customers in period 1. The

remaining buyers, between S1and the other seller, buy from the other seller. Suppose in period

2 you set a price of 140 ECU and the other seller sets a price of 120 ECU. A buyer at location

50 has costs of 190 ECU to both sellers. At this point, the cutoff is S2and all buyers between

your location and S2are buying from you. So you have 50 customers in period 2. The remaining

buyers between S2and 120 buy from the other seller.

Below is a graphical illustration and the calculation of the profits:

your Location other Seller

0 120

your Customers

in Period 1

= 70

your Customers

in Period 2

= 50

Profit in Period 1 = (Price in Period 1 −Costs)·Customers in Period 1

= (100 ECU −50 ECU)·70 = 3500 ECU

Profit in Period 2 = (Price in Period 2 −Costs)·Customers in Period 2

= (140 ECU −50 ECU)·50 = 4500 ECU

Profit =Profit in Period 1 +Profit in Period 2 = 8000 ECU

[Treatment 2]

Suppose you set a price of 100 ECU in period 1 and all buyers up to cutoff S1 at point 70 buy from

you after comparing the price of the other seller. So you have 70 customers in period 1. Suppose

in period 2 you set a price of 120 ECU for your period 1 customers and the other seller sets a price

of 60 ECU for your period 1 customers. A buyer at location 30 has costs of 150 ECU to both

sellers. At this point, the cutoff is Sold

2and all buyers between your location and Sold

2are buying

from you. You therefore have 30 old customers. The remaining buyers between Sold

2and S1buy

from the other seller.

Now to the other seller’s period 1 customer segment. Suppose you set a price of 80 ECU for

the other seller’s period 1 customer and the other seller sets a price of 160 ECU for his period 1

customer. A buyer at location 100 now has costs of 180 ECU to both sellers. At this point is the

cutoff Snew

2. All buyers between S1and Snew

2buy from you, forming your 30 new customers. The

2.7. TRANSLATED INSTRUCTIONS AND REVIEW QUESTIONS

remaining buyers between Snew

2and 120 buy from the other seller. Below is a graphical illustration

and the calculation of the profits:

your Location other Seller

0 120

your Customers

in Period 1

= 70

your old Customers

in Period 2

Sold

= 30

your new Customers

in Period 2

Snew

= 100

Profit in Period 1 = (Price for Period 1-Customers −Costs)·Period 1-Customers

= (100 ECU −50 ECU)·70 = 3500 ECU

Profit in Period 2 = (Price for old Customers −Costs)·old Customers

+ (Price for new Customers −Costs)·new Customers

= (120 ECU −50 ECU)·30

+ (80 ECU −50 ECU)·30 = 3000 ECU

Profit =Profit in Period 1 +Profit in Period 2 = 6500 ECU

[Treatment 3]

Suppose all buyers up to cutoff S1at location 70 are considered your adjacent customers after

period 1. Suppose in period 2 you set a price of 120 ECU for your adjacent customers and the

other seller sets a price of 60 ECU for your adjacent customers. A buyer at location 30 has costs

of 150 ECU to both sellers. At this point, the cutoff is Snear

2and all buyers between your location

and Snear

2are buying from you. They therefore you have 30 near customers. The remaining buyers

between Snear

2and S1buy from the other seller.

Now to the segment of the other seller’s adjacent customers. Suppose you set a price of 80

ECU for the other seller’s adjacent customers and the other seller sets a price of ECU 160 for his

adjacent customers. A buyer at location 100 now has costs of 180 ECU to both sellers. At this

point is the cutoff Sfar

2. All buyers between S1and Sfar

2buy from you, making up your 30 far

customers. The remaining buyers between Sfar

2and 120 buy from the other seller. Below is a

graphical illustration and the calculation of the profits:

your Location other Seller

0 120

your adjacent Customers

in Period 1

= 70

your near Customers

in Period 2

Snear

= 30

your far Customers

in Period 2

Sfar

= 100

2.7. TRANSLATED INSTRUCTIONS AND REVIEW QUESTIONS

Profit = (Price for near Customers −Costs)·near Customers

+ (Price for far Customers −Costs)·far Customers

= (120 ECU −50 ECU)·30

+ (80 ECU −50 ECU)·30 = 3000 ECU

[End Treatments]

Note that the prices for the example were generated randomly.

How do I get paid?

Your profit for the entire experiment is your cumulative profits across all rounds. At the end of the

experiment your earnings are converted into euros at the rate [Treatment 1 / Treatment 2] 3000

ECU = 0.10 Euro [Treatment 3] 1000 ECU = 0.10 Euro [End Treatments]. This amount will be

paid to you privately and in cash after the experiment, together with an entry fee of 5 Euro. In

the event that you made losses throughout the experiment, these will be offset against the entry fee.

Once you have finished reading the instructions, please raise your hand.

Review Questions

Before the experiment starts, it should be ensured that all participants have understood the in-

structions of the experiment. Your answers will not affect your payout and you can always ask

questions. To do this, please raise your hand and wait for someone to come to you to answer your

question. Once you have finished answering the questions, please raise your hand. An experimenter

will come to you and check your answers.

[Treatment 1]

Question 1. Suppose given the prices in period 1, all buyers up to the cutoff S1= 80 have bought

from you. In period 2 you set a price of 150 and the other seller sets a price of 130. Where is the

cutoff S2?

Question 2. After the second period there are the following cutoffs:

S1= 60,S2= 20

In period 1 you have customers

In period 2 you have customers

Question 3. Suppose you have costs of 50 ECU per unit sold and you set the following prices:

Price in period 1= 150 ECU

Price in period 2= 100 ECU

In period 1, 50 customers buy from you. In period 2, 40 customers buy from you.

Your profit for the entire round is:

[Treatment 2]

Question 1. Suppose given the prices in period 1, all buyers up to the cutoff S1= 80 have bought

from you. In period 2 you set a price of 150 for old customers and the other seller sets a price of

130 for new customers. Where is the cutoff Sold

2.7. TRANSLATED INSTRUCTIONS AND REVIEW QUESTIONS

Question 2. After the second period there are the following cutoffs:

S1= 60,Sold

2= 20 und Snew

2= 90

In Period 2 you have old customers and new customers

Question 3. Suppose you have costs of 50 ECU per unit sold and you set the following prices:

Price for Period 1-Customers= 150 ECU

Price for your period 1-customers in period 2 = 150 ECU

Price for the period 1-customers of the other seller in period 2 = 100 ECU

In period 1, 60 customers buy from you. In period 2, 30 old customers and 20 new customers buy

from you. Your profit for the entire round is:

[Treatment 3]

Question 1. Which of the following statements about the cutoff S1is true?

a) The cutoff S1is determined based on prices from the previous round.

b) Within the experiment, the participants have no influence on the cutoff S1.

Question 2. Suppose after period 1 all buyers up to cutoff S1= 80 are considered your ad-

jacent customers. In period 2 you set a price of 130 for your adjacent customers and the other

seller sets a price of 150 for your adjacent customers. At what point is the intersection point Snear

Question 3. After the second period there are the following cutoffs:

S1= 60,Snear

2= 20 und Sfar

2= 90

In Period 2 you have near customers and far customers

Question 4. Suppose you have costs of 50 ECU per unit sold and you set the following prices:

Price for near customers in period 2 = 150 ECU

Price for far customers in period 2 = 100 ECU

After period 2 you have 30 near customers and 20 far customers.

Your profit for the entire round is:

[Treatment 1 / Treatment 2]

Question 4. Which of the following statements about the other seller is true?

a) Within a round (consisting of two periods), the other seller is the same participant.

b) For the entire duration of the experiment, the other seller is always the same participant.

c) For each round, one participant in the experiment is randomly chosen as the other seller.

[Treatment 3]

Question 5. Which of the following statements about the other seller is true?

a) Within a round (consisting of two periods), the other seller is the same participant.

b) For the entire duration of the experiment, the other seller is always the same participant.

c) For each round, one participant in the experiment is randomly chosen as the other seller.

[End Treatments]

Chapter 3

We Value Your Privacy:

Behavior-based Pricing Under Endogenous Privacy13

3.1 Introduction

With an increased capability to process big data and the passing of EU’s Gen-

eral Data Protection Regulation (GDPR), behavior-based price discrimination and

consumer privacy have become a hot topic. Firms use consumers’ data to price

discriminate between them. The first major online test of behavior-based price

discrimination was conducted by Amazon more than twenty years ago (Streitfeld,

David, 2000). The company discriminated between consumers based on the num-

ber of previous purchases at Amazon. Since then consumers’ (personal) data has

been used for behavior-based pricing in online retailing. Evidence for such price dis-

crimination in e-commerce but also for discrimination in web searches were found by

Mikians et al. (2012, 2013) in an online field experiment. They show that consumers’

location and budget were used to price discriminate between them.

A lot has changed in the field of data protection and privacy since Amazon’s test

run. Particularly, the passing of the GDPR in May 2018 was a major breakthrough

for privacy protection. In accordance with the regulation, consumers can now de-

cide whether to allow websites to access their personal information (Parliament and

Council of the European Union, 2016). To gather information about consumers and

their online activities sellers can for example use cookies on their websites. The

collected data can be used by sellers to make offers in line with behavior-based pric-

13This chapter is the manuscript published as: Heiny, F., Li, T., and Tolksdorf, M. (2023).

We Value Your Privacy: Behavior-based Pricing Under Endogenous Privacy. Available at SSRN

3508762.

3.1. INTRODUCTION

ing. However, the GDPR gives consumers control over their personal information

by giving the the choice to opt-out and not reveal their data. If consumers hide

their data, it cannot be accessed by firms and thus consumers are anonymous. Con-

versely, if consumers share their data with a seller, it is available to the website and

thus consumers can be recognized and targeted with customized prices. This choice

to opt-out allows consumers to act strategically.

In this article, we study whether and under which conditions consumers share

their data with an online seller who can use the recorded data for price discrimi-

nation. Furthermore, we analyze the pricing strategy of the seller given the con-

sumers’ privacy choice. Following Fudenberg and Tirole (2000), we build on the

Hotelling (1929) linear city model with two competing firms and a continuum of

consumers. We consider a two-period game, where a consumer buys one unit of a

non-durable product in each period from one of the firms. In the first period, sellers

set identical prices for all consumers since they have no information on consumers.

Consumers then decide from which seller to buy and whether to share or hide their

data. In the second period, based on consumers’ first-period purchase histories and

privacy decisions, firms can set differentiated second-period prices for consumers.14

We contribute to the existing literature by contrasting two data policies, to check

how different data policies affect consumers’ and firms’ strategies and ultimately to

understand drivers of the privacy choice. First, we study a hypothetical open data

policy, where given a consumer shares their data, both firms gain access to the

consumer’s information about their previous purchase. That is to say, that firms

are mandated to share the consumer’s data.15 Even though such an open data

policy is hard to imagine, Article 20 of the GDPR gives consumers the right to data

portability, so that they can make their data available to more than one controller.

Therefore, the open data policy is possible in principle, even though practicability

would need to be explored first.16 Second, we analyze the current policy framework

resulting from the GDPR, where only the seller a consumer bought from can access

their data given the consumers shared their data. We refer to this environment as

exclusive data policy, since the data is exclusive to the firm a consumer purchases

from.

14We will restrict our attention to purchase histories as any information relating to an identified

or identifiable person is considered ‘personal data’ according to Art. 4 (1) of the GDPR. Bourreau

and De Streel (2018) find that there is no empirical evidence for actual personalized pricing, though

technically feasible, that goes further than price discrimination based on broad information.

15Generally, the EU’s data strategy calls for more data sharing between businesses. So far this

includes only non-personal data. However, our results suggest that from an antitrust perspective

it might be worth looking at such an open data policy.

16Ghosh et al. (2015) show a concrete example in which information is shared via cookie match-

ing.

3.1. INTRODUCTION

In the first part of this article, we develop a theoretical model of behavior-based

pricing with consumers’ endogenous privacy choice. Under both data policies we

solve our theoretical model for pure-strategy equilibria that determine consumers’

strategies concerning their privacy choice and firms’ price setting. In the second

part, we test our theoretical results in a laboratory experiment with human subjects

as buyers and sellers.17 We explore whether subjects follow our predicted strategies

from the theoretical model. In the experiment, we want to observe whether con-

sumers act rationally in their privacy choice since previous experimental literature

has shown that subjects value their data privacy in itself and therefore make behav-

ioral decisions when presented with the choice to reveal data (Acquisti et al., 2016;

Schudy and Utikal, 2017). Both the theoretical and the experimental aspect of the

analysis are important to comprehend how firms adapt their pricing to different data

policies and to understand how this changes consumers’ behavior towards their data

privacy. The theoretical analysis gives us an insight on firms’ and consumers’ opti-

mal behavior, while the experiment provides evidence of actual consumer behavior.

In the open data policy, when consumers’ data are available to both sellers,

consumers in equilibrium choose to share their data, which increases competition

between firms.18 Firms use the data to price discriminate between loyal consumers

and consumers, who previously purchased from the competitor. We can confirm this

result with experimental evidence from the open data treatment. Buyers predom-

inantly allow tracking of their past purchase, which gives sellers the chance to use

behavior-based pricing. We observe that sellers use poaching prices that are lower

than prices for loyal or anonymous customers as reward for sharing data.

In the exclusive data policy, when consumers’ data are only available to the

respective firm they bought from, all consumers anonymize in equilibrium. Even

though, as under the open data policy, sharing data amplifies competition between

firms, consumers are individually worse off by revealing their data. Due to the

exclusive data policy poaching prices are equal to prices for anonymous consumers,

whereby loyal consumers pay a mark-up when sellers price discriminate. Consumers

are individually best off by not sharing their data to avoid these loyalty mark-

ups. Yet, if consumers collectively coordinated to share their data, they would

improve their outcome.19 To our knowledge, this is a novel finding in competitive

settings with privacy decisions. In our experiment, we find that consumers initially

17To realize our experiment, we only need to discretize the number of consumers compared to

the theory. Hence, the experiment closely resembles our theoretical model.

18Ali et al. (2019) and Casadesus-Masanell and Hervas-Drane (2015) also support this result in

their theoretical models.

19The privacy choice resembles a multi-player prisoners’ dilemma in the exclusive data policy.

3.1. INTRODUCTION

share their information readily, while sellers do not use the information to price

discriminate. However, when sellers begin to employ poaching strategies, i.e. to

charge loyalty mark-ups, there is a downwards trend in the data sharing rate of

buyers. This is indicative of our theoretical prediction.

Finally, we discuss welfare and find from a theoretical point of view, that social

welfare is maximal under the exclusive data policy, even though it hurts consumers.

In equilibrium, all consumers choose to be anonymous and, therefore, firms set uni-

form prices. In this equilibrium consumers do not switch between firms such that

the market is efficient. On the other hand, consumer welfare is larger in the open

data policy in equilibrium, because consumers benefit from poaching offers. In our

experiment we observe poaching discounts that lead to an increase in inefficient

switching. This indicates that an open data policy can be an option to enhance

competition between firms but may come at a loss of social welfare. Our theoretical

and experimental results show that mandated data sharing among firms leads con-

sumers to share more data to their own benefit, providing an argument in favor of

an open data mandate under a consumer surplus oriented approach.

3.1.1 Related Literature

Our paper is related to a set of articles in the theoretical and the experimental

literature on behavior-based price discrimination and consumer privacy.

The following articles also study an endogenous privacy choice of consumers:

Conitzer et al. (2012), Ali et al. (2019), Acquisti and Varian (2005), Casadesus-

Masanell and Hervas-Drane (2015), Rhodes and Zhou (2021) and Anderson et al.

(2019).

Conitzer et al. (2012) study a monopoly with an outside option where consumers

can choose to let the monopolist track their purchases. They find that under free

anonymization all consumers choose to do so, which gives the monopolist the highest

payoff. Importantly, the introduction of competition raises issues in the handling of

the information structure, which leads to our separation of the open and exclusive

data policies. As in our paper, consumers have an endogenous privacy choice. How-

ever, Conitzer et al. (2012) do not study a competitive situation of behavior-based

pricing, where the strategic action of consumers has different implications for pric-

ing. Our focus is on consumers’ privacy choice for different data policies, in which

we diverge from the theoretical analysis of Conitzer et al. (2012).

Ali et al. (2019) study how complete consumer control over their data affects

personalized pricing in a monopoly as well as under competition. They focus on

comparing disclosure channels and analyze consumers sharing rich and simple ev-

3.1. INTRODUCTION

idence about their types. In our model we only look at a dichotomous disclosure

technique, tracking versus no tracking, but support the same result, that voluntary

disclosure amplifies competition under an open data policy. However, the opposite

occurs under an exclusive data policy.

Differing from our paper Acquisti and Varian (2005) only consider two con-

sumer types instead of a continuous differentiation and undifferentiated products.

Casadesus-Masanell and Hervas-Drane (2015) consider homogenous goods in a one-

period model, where information is provided directly by consumers and not indirectly

in form of their purchase history. Rhodes and Zhou (2021) consider personalized

pricing in shared data environments similar to our open data policy. They find that

data sharing by consumers imposes a negative externality to other consumers, in

contrast to the positive externality that we depict in our exclusive data policy. In

line with our results under an open data policy they find that competition is in-

tensified at the harm of firms and to the benefit of consumers, unless the market

is not fully covered. Anderson et al. (2019) also consider personalized pricing and

allow consumers to share their data with all firms, similar to our open data policy.

Similar to Rhodes and Zhou (2021) they find that data sharing imposes a negative

externality but in contrast to them they find that both firms and consumers benefit

from the opt-in policy. Our main contribution over these studies is that we analyze

how different data policies shape market outcomes, given that a data regulation is

already in place.

Colombo (2016) considers a set-up of incomplete information sharing in a duopoly

case similar to our exclusive data policy (in Section 3.2.2). Colombo uses a fixed pa-

rameter as share of anonymous consumers and does not consider consumers’ endoge-

nous privacy choice. Belleflamme and Vergote (2016) employ a similar parameter as

the precision of the tracking technology in a monopolistic setting with endogenous

privacy choices as in Conitzer et al. (2012) but without repeat purchases. The main

point of our study, however, is to analyze the strategic decisions of consumers in a

duopolistic setting with repeat purchases over two periods. Other papers that are

also concerned with price discrimination and exogenous privacy are Liu and Serfes

(2004); Esteves (2014).

Taylor (2004); Montes et al. (2018); Choi et al. (2019) extend the idea of price

discrimination and privacy to include a data broker. Montes et al. (2018) consider

a duopoly with a costly privacy choice for consumers. They focus on a data broker

who sells consumers’ data to competing firms. One of their main results is that

information is usually only sold to one of the firms. We feature this as the exclusive

data policy, where we observe a higher producer surplus than in the open data policy.

3.1. INTRODUCTION

Choi et al. (2019) study the stage of data collection and show that either due to

a monopolistic platform or due to the emergence of data brokerage an excessive

amount of data is collected to the detriment of consumers. In contrast to these

studies, we do not include data brokers in our model, but consider the direct channel

between consumers and firms.

Extensive reviews of the literature on behavior-based price discrimination in

general and the economics of privacy can be found in Armstrong (2006b); Fudenberg

and Villas-Boas (2006b); Esteves et al. (2009); Acquisti et al. (2016).

The experimental analysis of behavior-based pricing under endogenous privacy

relates to two branches in the experimental literature. Firstly, the basic structure

and procedure are related to spatial competition experiments. We extend the exist-

ing literature on behavior-based price discrimination and spatial competition with

location choice experiments. Behavior-based pricing experiments have been con-

ducted by Brokesova et al. (2014b) and Mahmood (2014b). Brokesova et al. (2014b)

computerize the buyer’s side, which we do not. Mahmood (2014b) only considers

two fixed locations for buyers, whereby the experimental market rather resembles a

Bertrand market with differentiated products than a spatial competition. We em-

ploy a behavior-based pricing experiment similar to those two but introduce features

from spatial competition with location choice experiments by Camacho-Cuena et al.

(2005) and Barreda-Tarrazona et al. (2011), which is how we transform the theo-

retical set-up into an experimental set-up with treatments corresponding to the two

data policies.

Secondly, we introduce privacy and data sharing elements. Similar issues have

been studied before, but to our knowledge not in the context of an explicit market

experiment. Acquisti et al. (2013) identify a considerable gap between willingness to

accept disclosure of private information and willingness to pay for the protection of

private information. To alleviate this issue we renounce enforcing a default option

on privacy, assuming disclosure and protection are both costless. Beresford et al.

(2012); Preibusch et al. (2013) find that subjects have a remarkably low willingness-

to-accept for giving up their privacy and are not acting on their stated privacy

decisions when protection of privacy is costless. This finding contrasts Tsai et al.

(2011) who find that subjects act on websites’ certified privacy protection qualities

when shopping online. They suggest that subjects might in fact be willing to pay

premiums for privacy protection.

Schudy and Utikal (2017) find that subjects’ willingness to share personal in-

formation decreases when the number of recipients of said information increases.

Between our open and exclusive data treatments the number of recipients varies.

3.2. THEORY

In support of their findings, we observe a higher willingness to share information in

the early rounds of the exclusive data treatment. In later rounds we observe more

information sharing in the open data treatment, which is in line with our theoretical

predictions. This indicates that participants see the privacy decision as a strategic

choice, which allows them to face lower prices.

We contribute to the experimental privacy literature by focusing on consumers’

endogenous privacy decisions in competitive markets under different data policies,

where the private information arises endogenously within the context of the game.

Combining a theoretical model with an experiment is a novel approach to answer

our research questions.

3.2 Theory

In this part of the article, we present our theoretical model and the results from the

analysis. First, we introduce the model set-up. Next, we analyze our theoretical

model under the open data policy, where information about previous purchases is

available to both firms. This is followed by the analysis of the exclusive data policy,

where only the firm that a consumer has bought from in the first period can access

consumers’ data. Finally, we state welfare results from the theoretical model.

3.2.1 Model

We consider a set-up following Hotelling (1929), where a line segment of length ¯

spans a product characteristic space. Along the line, consumers are uniformly dis-

tributed with a density of ¯

θ−1, i.e., we assume a consumer mass of one. A consumer’s

type is denoted by θ∈[0,¯

θ], such that θserves as the consumer’s preferred variety

of a good.

There are two firms each producing a variant of the same good at constant

marginal costs normalized to zero; fixed costs are neglected. We normalize produc-

tion costs because we do not focus on firms’ production processes. Firm Ais located

at the left end of the line segment, while firm Bis placed at the right end. The

firms compete for two periods, t= 1,2.

In each period, consumers buy one unit of the good either from firm Aor B,

bt∈ {A, B}, i.e., we assume that the good’s valuation is large enough to make

sure each consumer buys one unit in each period. No outside option is available.

Considering a consumer located at ˆ

θ, their utility is given by UA=v−pA−ˆ

θor

UB=v−pB−(¯

θ−ˆ

θ), depending on their purchasing decision. We assume consumers’

unit transportation cost to be normalized to one. Consumers’ valuations, v, are the

3.2. THEORY

same over time for all consumers. Their rationale is to maximize their utility. We

do not take discounting into account to simplify the analysis.

On top of the buying decisions, bt, consumers also decide whether to share their

data, q∈ {0,1}, in the first period. If q= 1, i.e., a consumer decided to reveal their

data of the first-period purchase, a firm is able to recognize according consumer

groups who made similar decisions and can thus adjust the price for the second

period. In the literature, it is often assumed that generating privacy involves some

costs (Conitzer et al., 2012; Montes et al., 2018). However, Loertscher and Marx

(2020) show that the act of providing data can also be costly for consumers. Thus,

we refrain from assumptions on privacy costs to keep the theoretical predictions

clean from any of these effects. This is important for the experiment, because we

can then observe subjects’ unbiased privacy concern.

In the first period, competing firms set price pi

1, where i, j =A, B and i=j.

In the second period, pricing is more involved. Depending on the preceding privacy

choice of consumers, there is a share λof anonymous consumers who hid their

data and a share 1−λof recognizable consumers. The shares are derived from

the aggregation of consumers’ choices regarding their data. We assume that λis

common to both firms.

Given the privacy choice of a consumer, we differentiate between two data poli-

cies, which differ with regards to the number of recipients of consumers’ data. The

information about consumers’ buying decision in the first period is either available

to both firms, which we refer to an open data policy, or a firm exclusively receives

the information, which we call exclusive data policy.

In the open data policy, both firms observe the past purchase of all consumers

who shared their data and can distinguish them by purchasing decision. In the

exclusive data policy, each firm observes the past purchase of consumers who shared

their data and bought from them, while consumers who shared their data and bought

from the other firm are indistinguishable from anonymous consumers.

In the open data policy, where both firms can target the competitor’s consumers,

each firm sets three prices in the second period: pi

2,i, is firm i’s loyalty price for

identifiable consumers who bought from firm iin the first period; pi

2,j, is firm i’s

poaching price for recognizable consumers who bought from jin the first period; and

2, is firm i’s new customer price for anonymous consumers who belong to the share

λ. Under the exclusive data policy, firms cannot target the competitor’s consumers.

This alters the pricing strategy in that firms can no longer set a poaching price pi

2,j.

Figure 3.1 depicts the timing of the game. At the beginning, each consumer

learns their type θ. Then, in the first period, firms each set price pi

1. Afterwards,

3.2. THEORY

Consumers learn

type, θ∈0,¯

θ

Firms set

Consumers make

1st purchase, b1∈ {A, B}

and privacy choice q∈ {0,1}

Firms set

2,i, pi

2,j, pi

Consumers make

2nd purchase, b2∈ {A, B}

Figure 3.1: Timeline of the game.

consumers simultaneously make their purchasing decision, b1∈ {A, B}and their

privacy choice, q∈ {0,1}. In the second period, firms set prices p2= (pi

2,i, pi

2, pi

2,j).20

At the end of the second period, consumers again choose to buy from Aor B. Finally,

consumers receive their utilities and firms earn profits.

We solve for perfect Bayesian Nash equilibria (PBE) in pure strategies. In this

context, a PBE comprises firms’ and consumers’ strategies. Firms’ strategies contain

first- and second-period prices for the respective data policy and their beliefs about

consumers’ types given their privacy choice.21 Consumers’ strategies contain their

first purchase and the privacy choice dependent on their type, firms’ first-period

prices and anticipation of optimal second-period prices and their second purchase

dependent on their type and second-period prices.

3.2.2 Endogenous Privacy

In this section, we analyze our theoretical model and solve for PBE.22 The potential

equilibria can be categorized into pooling and separating equilibria based on the

consumer’s privacy choice and their type. In a pooling equilibrium, all consumers

make the same privacy choice independent of their type. The share of anonymous

consumers λis the overall share of consumers who choose to keep their past purchase

hidden. Analogously, 1−λ, corresponds to the share of consumers who reveal their

data. In a separating equilibrium, consumers base their privacy choice on their

type. This means, that firms can form beliefs over any number of segments of

arbitrary length where within each segment consumers either all disclose or all hide

their information (due to pure strategy). We consider the two possible equilibrium

categories one after another, starting out with deriving possible equilibria under

pooling beliefs of firms. We relax pooling beliefs, respectively separating beliefs,

once we identify equilibrium candidates.

20There is no poaching in the exclusive data policy, which is equivalent to inducing pi

2,j ≡pi

21The strategy should also contain second-period prices if firms had set different prices in the

first period. This is omitted here for simplicity.

22We restrict our analysis to pure strategy equilibria due to intractability of mixed strategy

specifications.

3.2. THEORY

Open data policy

Under the open data policy, both firms receive information about a consumer’s

previous purchase given the consumer decides to share their data. Consumers who

did not share their data in the first period, are anonymous to both firms and are

treated as new consumers. Therefore, they face prices pA

2(pB

2) from firm A(firm B)

in the second period. Consumers who revealed information about the purchase in

the first period can be recognized by firms and thus are offered different prices in the

second period. The prices pA

2,A (pB

2,A) are offered by firm A(firm B) for consumers

who bought from firm Ain the first period, and pB

2,B (pA

2,B) are set by firm B(firm

A) for consumers who bought from firm Bin the first period. We first analyze the

open data policy under pooling beliefs of firms, i.e., firms believe that consumers

make their privacy choice independent of their location. Therefore, we can divide

consumers by their privacy choice into recognizable and anonymous consumers and

consider two separate Hotelling lines according to the groups.

On the anonymous consumers’ line, there are λconsumers uniformly distributed.

On this line, there exists a marginal consumer, θ2, who is indifferent between buying

from firm Aand firm Bat prices pA

2and pB

2, respectively. Therefore, consumers with

type θ∈[0, θ2)buy from firm Ain the second period given they chose to anonymize.

Similarly, consumers with θ∈(θ2,¯

θ]buy from firm B.

The other line has a mass of 1−λuniformly distributed and recognizable con-

sumers. They are confronted with behavior-based price discrimination. Among the

mass of 1−λconsumers, those who bought from firm Ain the first period are offered

the good at two different prices in the second period: pA

2,A as loyalty price set by

firm A, and pB

2,A as a poaching price from firm B. Similarly, consumers who bought

from firm Bin the first period also face two prices now, pB

2,B as loyalty price from

firm B, and pA

2,B as a poaching price from firm A.

On the line of recognizable consumers, there are two marginal consumers: one on

A’s turf and one on B’s turf. The marginal consumer on A’s turf, θA

2, is indifferent

between buying from firm Aat pA

2,A and buying from firm Bat pB

2,A. Accordingly,

on B’s turf, the marginal consumer, θB

2, is indifferent between buying from firm B

at pB

2,B and buying from firm Aat pA

2,B. Recognized consumers of type θ∈[0, θA

and θ∈(θB

2,¯

θ]are loyal to the firm they bought from in the first period. Contrarily,

consumers located at θ∈(θA

2, θ1)and θ∈(θ1, θB

2)are poached by the competing

firm, where θ1denotes the first-period marginal consumer who is indifferent between

buying from Aand B.

Figure 3.2 depicts the two Hotelling lines of anonymous and recognizable con-

sumers in the second period. For the share of anonymous consumers, λ, the line of

3.2. THEORY

length ¯

θis divided by the marginal consumer θ2. To the left of it, consumers buy

from A, to the right, they buy from B. For the share of recognizable consumers,

1−λ, the line is divided by marginal consumers θA

2,θB

2and θ1. To the left of θA

2and

to the right of θB

2consumers are loyal to their seller and buy from the respective

same firm again in the second period. However, to the right of θA

2and to the left of

θB

2, consumers are being poached in the second period.

Firm A

Firm B

θ1

θA

2θB

θ2

2,A pB

2,A pA

2,B pB

2,B

2pB

Figure 3.2: consumer segments under open data in t= 2.

Solving firm Aand B’s maximization problem for the line of anonymous con-

sumers, the second-period new consumer prices are pA

2=pB

2=¯

θ. That is, Aand

Bset a uniform price because they receive no information from consumers. Conse-

quently, the marginal consumer who is indifferent between buying from Aand Bis

located at the center of the line at θ2=¯

2. The second-period prices for consumers

who revealed their data are displayed in the following Lemma.

Lemma 1 Loyalty and poaching prices for consumers, who decided to reveal their

data, depend on θ1and the parameter ¯

θ.

Loyalty prices are given by

2,A =⎧

⎨

⎩

3(2θ1+¯

θ)if 1

4¯

θ≤θ1

θ−2θ1otherwise

, pB

2,B =⎧

⎨

⎩

3(3¯

θ−2θ1)if 3

4¯

θ≥θ1

2θ1−¯

θotherwise

Poaching prices are given by23

23When θ1<1

4¯

θit follows that pB

2,A = 0, and so Firm A sets pA

2,A such that v−pA

2,A −θ1=

v−(¯

θ−θ1). Accordingly for firm B, when θ1>3

4¯

θit follows that pA

2,B = 0, and thereby Firm B

sets pB

2,B such that v−θ1=v−pB

2,B −(¯

θ−θ1).

3.2. THEORY

2,B =⎧

⎨

⎩

3(3¯

θ−4θ1)if 3

4¯

θ≥θ1

0otherwise

, pB

2,A =⎧

⎨

⎩

3(4θ1−¯

θ)if 1

4¯

θ≤θ1

0otherwise

New consumer prices are pA

2=pB

2=¯

θ.

Proof. See Appendix.

Lemma 1 shows that if a consumer chooses not to share their information in the first

period, they will face uniform pricing in the second period under a pooling assump-

tion. However, if they reveal information in the first period, they are confronted with

behavior-based prices, including poaching prices offered by the competitive firm in

the second period. Lemma 1 demonstrates that prices are independent of λ. There-

fore, under pooling beliefs the result pi

2> pi

2,i > pi

2,j holds generally, irrespective of

θ1∈(0,¯

θ).

Looking at the first period, we study consumers’ endogenous decisions about

their data privacy. By comparing second-period prices for anonymous consumers to

second-period prices for recognized consumers, we can show that prices for anony-

mous consumers are always higher. Consumers can strategically choose to share

their purchasing history in the first period, in order to receive lower prices in the

second period. Thus, every consumer discloses their information, which implies that

the mass λof consumers on the anonymous line is zero. Firms form their beliefs

accordingly.

Finally, we consider price setting of firms in the first period. Similar to the

second period, there are two separated lines in the first period. For the line of

consumers who did not reveal their data, there is a cut-off consumer, ˆ

θ1, who, in the

first period, is indifferent between buying from firm Aat pA

1and buying from firm

Bat pB

1.24

On the other hand, on the line of those who shared their data in the first period,

the marginal consumer, θ1, is indifferent between buying from firm Aat pA

1in the

first period and afterwards from firm Bat pB

2,A in the second period, and buying

from firm Bat pB

1in the first period and afterwards purchasing from firm Aat pA

2,B

in the second period.

In the first period, firms maximize the overall profits from the first and sec-

ond period. Solving the maximization problems under consideration of consumers’

privacy choices yields our first proposition.

24 ˆ

θ1is not influenced by second-period prices, since the share of those who did not disclose

their information is λ, and the two because firms maximize their profits by choosing new customer

prices, pA

2and pB

2, which are independent of the first period.

3.2. THEORY

Proposition 1 The prices under open data for the competing firms in both periods

are

1=pB

1=4

3 + λ¯

θ, pA

2,A =pB

2,B =2

3¯

θ, pA

2,B =pB

2,A =1

3¯

θ.

The marginal consumer in the first period is located at θ1=¯

2. Consumers’ strategy

is to disclose data such that λ= 0 ∀θ. Therefore, we obtain a symmetric PBE in

pure strategies.

Proof. See Appendix.

Proposition 1 shows firms’ price choices and consumers’ privacy choice, λ, in equi-

librium for pooling beliefs. Consumers choose to share their data, λ= 0, since they

face lower prices as recognized consumers in the second period than if they were

anonymous. Therefore, firms’ prices for anonymous consumers are not realized in

equilibrium. The prices in Proposition 1 are symmetric for firm Aand Bbecause

the marginal consumer, θ1, is located in the center of the Hotelling line, such that

each firm’s turf is of equal size. Notice that firm A’s (respectively firm B’s) poach-

ing price is lower than the price for the loyal consumers.25 The first-period prices

depend on consumers’ privacy choice. If λ= 1, which means that none of the con-

sumers grants access to their data in the first period, this results in a uniform pricing

strategy, pA

1=pB

1=¯

θ. If on the other hand λ= 0, which means that all consumers

share their information in the first period, we get that pA

1=pB

1=4

3¯

θ, which is a

standard behavior-based pricing strategy. Therefore, all values of λ∈(0,1),pA

1and

1represent a mixture of uniform pricing and behavior-based pricing.

We derive the equilibrium in Proposition 1 under pooling beliefs. In the proof of

Proposition 1 we use a refinement argument, relaxing pooling beliefs, to show that

an individual deviation from consumers’ privacy choices is not desirable. Lastly,

we inspect whether there are alternative equilibria under separating beliefs, where

consumers base their privacy choice on their type. We check for potential equilibria

in pure strategies. The results are summarized in the following proposition.

Proposition 2 No pure-strategy separating equilibrium exists under the open data

policy. The pooling equilibrium derived above is unique in pure strategies.

Proof. See Appendix.

25Surprisingly, we find the same pricing and privacy choices when consumers are myopic in

their first-period purchasing decision, but strategic in their privacy choice. This indicates that

the privacy choice absorbs the strategic properties of the first-period purchasing decision. When

transportation costs are quadratic we find qualitatively similar pricing choices and the same privacy

choices as in the case of linear transportation costs. See Appendix.

3.2. THEORY

Proposition 2 states that under the open data policy the equilibrium derived in

Proposition 1, where all consumers reveal their information, is unique. In the proof

of Proposition 2 we assume towards a contradiction that there exists an equilibrium

under which firms believe that consumers make their privacy choice based on their

type. To this end, we separate the Hotelling line into segments where consumers

either share or hide their data and check whether any segmentation by privacy choice

leads to an equilibrium. However, this is only incentive compatible for consumers

when prices are non-discriminatory, while it is not incentive compatible for sellers to

post non-discriminatory prices. Therefore, no equilibrium under separating beliefs

exists.

From the results in Propositions 1 and 2 we gather that an open data policy

leads to identical results as in standard behavior-based pricing with exogenous pri-

vacy where competitors do not share information (see Fudenberg and Tirole, 2000).

Consumers are best off by revealing data, because they can benefit from the lower

customized prices in the second period.

Exclusive data policy

In this section, we analyze a policy where firms only access data of consumers who

actually bought from them. This implies that there is exclusive data in the market,

as for example consumers of firm B, might reveal their purchasing history to B,

such that Bcan recognize them. However, firm Adoes not receive the information

and therefore, these consumers are anonymous to A. The pricing strategy in the

second period is distinct from the open data policy, where three different prices were

set by each firm after consumers made a decision regarding their privacy choices.

In comparison under the exclusive data policy, firms cannot distinguish between

a competitor’s consumers and their own anonymous consumers. They are just a

mass of non-recognizable consumers. This implies that firms cannot set a poaching

price to attract consumers from each other. The pricing strategy for the second

period only entails a loyalty price, pi

2,i, and a new consumer price, pi

2for i=A, B.

The first-period pricing is similar to the open data policy and not affected by the

difference in the data policy. As before, there is a marginal consumer in the first

period, θ1, who is indifferent between buying from Aand B.26

Under the exclusive data policy, the Hotelling lines cannot be separated as in the

open data policy. The reason is that the new consumer price serves two functions.

Firstly, it is the price for the own consumers who are not recognizable and secondly,

26The analysis is similar to Colombo (2016). However, the essential difference is that he treats λ

as an exogenous parameter, while we use it as proxy for consumers’ endogenous decisions regarding

the use of their data.

3.2. THEORY

it serves as a “poaching price” for competitors’ consumers. Figure 3.3 below depicts

this clearly, since pi

2appears in both segments. Firms want to maximize their profits

by choosing prices pi

2,i and pi

2for i=A, B in the second period. As before, we start

with pooling beliefs for firms. There is a share 1−λof consumers who choose to reveal

their data and a share λof consumers who hide their data, with λcorresponding

to the probability of hiding for every consumer. For the share λof anonymous

consumers there is an indifferent consumer located at θ2, who is impartial between

buying from Aat price pA

2and Bat price pB

2. For the recognizable consumers, there

is a marginal consumer in each firms’ turfs: θA′

2is indifferent between buying from

Aas recognizable consumer and buying from Bas anonymous consumer, whereas

θB′

2is the respective cut-off value on B’s turf. Figure 3.3 shows this consumer

segmentation and price setting in a rectangle, where the two horizontal lines are

connected by λ.

Firm A

Firm B

θ1

θA′

2θB′

θ2

2,A pB

2pA

2pB

2,B

2pB

Figure 3.3: consumer segments under exclusive data.

Maximizing the firms’ second-period profits results in the prices given in the

following Lemma.

Lemma 2 All second-period prices depend on λand p1. The prices for firm Aare

2(λ, p1) = (9 −2λ+ 5λ2)¯

θ−4(3 −λ)(1 −λ)θ1

3[4−(1 −λ)2],

2,A(λ, p1) = (3 + 10λ−λ2)¯

θ+ 2(3 −λ)(1 −λ)θ1

3[4−(1 −λ)2].

3.2. THEORY

For firm B:

2(λ, p1) = (−3 + 14λ+λ2)¯

θ+ 4(3 −λ)(1 −λ)θ1

3[4−(1 −λ)2],

2,B(λ, p1) = (9 + 2λ+λ2)¯

θ−2(3 −λ)(1 −λ)θ1

3[4−(1 −λ)2].

Proof. See Appendix.

The second-period prices in this case are not only dependent on the first-period

prices, as is the case in the analysis of the open data policy, but also depend on λ

as the share of buyers who choose to be anonymous.

All prices increase with λ, i.e., the more likely consumers are to hide their data,

the higher are not only the new consumer prices but also the loyalty prices of both

firms. This always holds for 1−λ

3−λ¯

θ≤θ1≤2

3−λ¯

θ. Under this condition, loyalty prices

are larger or equal to new consumer prices.27

Figure 3.4 depicts loyalty and new consumer prices of firm Afor ¯

θ= 1 and

θ1=1

2. At λ= 0, firms set symmetric prices with pA

2=pB

2=1

3and pA

2,A =pB

2,B =2

The price setting corresponds to poaching and loyalty prices in the open data policy,

respectively. Given λ→128 all prices converge to ¯

θ= 1, the uniform pricing strategy.

There is no price discrimination in this case since there is no information available.

The graph shows that prices are convex, increasing in λand within the range

of λ∈[0,1) loyalty and new consumer prices do not cross. Therefore, even though

the new consumer prices increase with λ, they are always below the loyalty prices.

In Figure 3.4, we observe a situation that is similar to the prisoner’s dilemma.

Consumers face the highest prices when λapproaches one. When λ= 1 only new

consumer prices are realized and correspond to uniform prices of one. On the other

hand, if consumers were to decide to hide their information with probability λ= 0,

this would lead them to a price of 2

3which is below one. This means, if consumers

can coordinate on putting zero probability on anonymizing, they would all gain.

However, consumers have an incentive to deviate to stay anonymous with a positive

probability, since for any λ∈(0,1) they face a new consumer price below the loyalty

price. This incentive leads all consumers to anonymize.

The two firms’ maximization problems are independent between the two periods

since consumers always anonymize. From this we find the equilibrium strategies

under the exclusive data policy, which are stated in the following proposition.

27When we derive first-period prices we show that the market is separated symmetrically be-

tween the firms such that the condition holds.

28Notice that for λ= 1, the loyalty prices are no longer contained in the maximization problems.

3.2. THEORY

0.2

0.4

0.6

0.8

1.0

0 0.2 0.4 0.6 0.8 1.0

Price

Loyalty price

New customer price

Figure 3.4: Prices of Firm Afor ¯

θ= 1 and θ1= 0.5.

Proposition 3 Under the exclusive data policy, consumers’ equilibrium strategy is

to hide their information, i.e., λ= 1. Therefore, final prices all coincide with the

uniform pricing strategy, such that prices on the first and second period are ¯

θ.

Proof. See Appendix.

The results of Proposition 3 are derived under the beliefs that consumers make their

privacy choice independent of their type. In the proof of Proposition 3 we use the

same refinement argument as before and find that there is no profitable individual

deviation, when relaxing the pooling beliefs. We have shown that consumers have

an incentive to hide their data due to lower new customer prices when their data

is exclusive to the firm that they have bought from. Because firms do not receive

any data, they set uniform prices in the first and second period. This is contrary

to the results in Proposition 1. Under the open data policy, consumers share their

data to increase competition between firms which results in lower prices for con-

sumers. However, under the exclusive data policy, sharing data leads to asymmetric

information since only the firm a consumer has bought from receives the data. This

firm can use the exclusive information to their advantage by setting a higher price.

Therefore, sharing data has opposing effects in the two data policies.

Same as in the analysis of the open data policy, we now check whether there is

an equilibrium when firms form separating beliefs. The results are summarized in

the following Proposition.

Proposition 4 No pure-strategy separating equilibrium exists under the exclusive

data policy. The pooling equilibrium derived above is unique in pure strategies.

3.2. THEORY

Proof. See Appendix.

Proposition 4 states that the equilibrium under exclusive data, in which all the con-

sumers hide their information is unique. As in Proposition 2, to prove Proposition 4

we assume towards a contradiction that there is an equilibrium under separating

beliefs. We separate the Hotelling line into segments by consumers’ privacy choice

and check for all possible segmentations whether there is an equilibrium. However,

we do not find an equilibrium under separating beliefs. Thus, the equilibrium in

Proposition 3 is unique. Combining Propositions 3 with 4 it follows that in the

unique equilibrium firms set uniform prices. Thus, the exclusive data policy yields

the same result as the benchmark case in Fudenberg and Tirole (2000), where price

discrimination is either prohibited or first-period buying decisions are not observ-

able.

While in the open data policy, consumers increase competition between firms

by revealing their data, here, consumers cannot influence competition between firms

with their privacy choice. Under the exclusive data policy, firms do not operate under

symmetric information when consumers reveal their data. Therefore, by sharing

information in this data policy consumers are worse off because firms can use the data

to price discriminate on them without needing to intensify competition. Under the

exclusive data policy, firms obtain larger profits since they do not receive information

about their consumers. Therefore, the firms cannot set customized prices but have

to conform to a uniform pricing strategy.

3.2.3 Welfare

In order to fully understand our results, we analyze consumer and producer surplus

as well as social welfare for both data policys. The theoretical analysis is based on

the equilibria we find in Proposition 1 and Proposition 3.

The producer surplus (profit) shows that in equilibrium firms prefer a setting

where data is not shared with a competitor as

π∗

open =17

18 ¯

θ2< π∗

excl. =¯

θ2.

The profits are larger in the equilibrium under the exclusive data policy. Consumers’

equilibrium strategy is to anonymize, hence firms set uniform prices in both periods.

Compared to the open data policy, prices are higher in the second stage of the

exclusive data policy, benefiting firms. In the open data policy, profits are lower

because in equilibrium consumers choose to share their data. This leads to an

increase in competition among the two firms. In our model, firms cannot commit to

3.2. THEORY

not use information about their consumers. Therefore, firms prefer a setting where

in equilibrium they do not receive any information about consumers.

For consumers the case is not as simple, since they receive different utilities based

on their type. Utilities are determined by the data policy and the buying decisions

over two periods. It matters whether consumers are loyal to a firm over both periods

or whether they were poached in the second period, i.e., they switch between firms.

The type-dependent equilibrium utilities for the different data policys are given in

the following terms:

U∗

open(θ) = ⎧

⎪

⎨

⎪

⎩

2(v−¯

θ−θ)for θ∈[0,¯

2v−8

3¯

θfor θ∈(¯

3,2¯

2(v−2¯

θ+θ)for θ∈(2¯

3,¯

θ]

U∗

excl.(θ) = ⎧

⎨

⎩

2(v−¯

θ−θ)for θ∈[0,¯

2(v−2¯

θ+θ)for θ∈(¯

2,¯

θ]

When comparing the utility levels for the different data policys, we find that con-

sumers obtain the same utility for θ∈[0,¯

3)and θ∈(2¯

3,¯

θ]in the open and exclusive

data policy, but they obtain a higher utility for θ∈(¯

3,2¯

3)in the open data policy.

Consumers who are located further away from the firms can benefit from behavior-

based pricing and receive a larger rent due to lower poaching prices that are available

to them.

From the utilities we can derive the consumer surplus for both data policies as

CSopen = 2v¯

θ−22

9¯

θ2, CSexcl. = 2v¯

θ−5

2¯

θ2.

We find that

CSopen > CSexcl.

Consumers and firms prefer opposing data policies. Consumers’ interest is to share

their data with all firms on the market because firms cannot commit to not use the

data. This increases competition between firms. On the other hand, firms benefit

from a situation in which each competitor keeps their consumers’ data to themselves.

The level of data available to firms drives the results.

The total welfare for both data policies is

Wopen = 2v¯

θ−5

9¯

θ2, Wexcl. = 2v¯

θ−1

2¯

θ2.

3.3. EXPERIMENT

From this follows

Wexcl. > Wopen.

The overall welfare level is higher under the firm-preferred, exclusive data policy.

The efficiency loss incurred by firms in an open data policy is larger than the loss of

consumers in an exclusive data policy. The welfare loss under open data comes from

inefficient switching, i.e., consumers that are poached do not buy from the closest

firm. While consumers gain from being poached, as can be seen in the comparison of

their utility levels, firms lose profits (compared to the exclusive data policy) because

of the lower poaching prices they set.

The theoretical analysis shows social welfare to be lower in the open data policy,

since sharing of data between firms incentivizes consumers to share their data and

to inefficiently switch between firms.

3.3 Experiment

As we have shown, our theory makes strong predictions towards consumers’ privacy

choices. It suggests that an open data directive could benefit consumers, while

probably doing so at cost of total welfare. However, this requires consumers to

be fully rational by choosing to share their data with firms under an open data

policy. Because consumers have an active role in the theoretical model it would

be desirable to empirically verify their behavior and check the implications of our

model. However, we cannot use real-world data because firstly, to our knowledge

there is no mandated open data directive in place and secondly, we would need to

gather data on consumers who may object to their data being gathered.

Due to these reasons we employ a laboratory experiment. This circumvents the

stated issues and allows us to i) fully control the data policy and ii) fully observe

whether and which data are disclosed by consumers.

3.3.1 Design

Our experimental design has two parts. The first and main part is a multi-stage

market game, closely resembling our theoretical set-up. In the second part we collect

additional measures to control for cognitive ability, privacy concern and demograph-

ics.

3.3. EXPERIMENT

Market game

Our implemented market game closely follows the theoretical set-up and aims at

testing our predictions concerning the buyers’ privacy choices and the sellers’ pricing

choices under the two data policies. Subjects take the role of buyers or sellers,

corresponding to consumers and firms in our theoretical model, with roles remaining

fixed for the duration of the experiment. Each market contains six buyers and two

sellers and lasts for two periods. A market is formed by eight adjacent locations, with

sellers being located at either end and six buyers in between on distinct locations as

depicted in Figure 3.5.

Theoretical representation:

1 2 3 4 5 6

Experimental representation:

Location 1

Location 2

Location 3

Location 4

Location 5

Location 6

Location 7

Location 8

Figure 3.5: Conversion of theoretical into experimental market.

Two markets are simultaneously formed within one matching group, with match-

ing groups consisting of six buyers and four sellers. Buyers are active in both markets

with locations drawn independently.29 Sellers are only active in one market and are

randomly located at location 1 or location 8, which corresponds to taking the role of

seller Aor seller B.30 This allows for a randomization of seller composition between

market rounds, so that markets are independent between rounds and resemble one-

shot interaction, while limiting the size of matching groups. In total there are 20

market rounds to allow participants to get acquainted with the market game.

Similar to Camacho-Cuena et al. (2005) and Barreda-Tarrazona et al. (2011)

we allow sellers to choose integer prices from the interval [0,10]. Buyers exert unit

transportation costs per unit of distance traveled.31 Under consideration of trans-

portation costs the price interval ensures that buyers never have negative earnings.

29According to Mahmood (2014b) buyer involvement increases when active in multiple markets

30In comparable seller-only experiments by Brokesova et al. (2014b), matching groups of four

were shown to be suitable.

31For example, a buyer at Location 6 has to bear transportation costs of five to buy from a

seller at Location 1.

3.3. EXPERIMENT

Our two treatment variations are (i)open data treatment and (ii)exclusive data

treatment according to the two data policies in our theoretical model.

The course of action follows the timeline of the theoretical model. Initially,

sellers choose the first-period price. Buyers then decide whether to purchase from

seller Aor Band whether to allow tracking of their purchase decision or not. Sellers

then learn the first-period price of their competitor and the number of buyers of both

sellers. They do not learn which or how many buyers allow tracking of their purchase.

By this we employ a fully belief-based interpretation of our theoretical model, with

beliefs not only governing the distribution, but also the share of anonymizing buyers.

In the second period of the open data treatment, sellers choose a loyalty price, a

poaching price and a new-customer price. In the second period of the exclusive data

treatment, sellers are limited to choosing a loyalty price and a new customer price.

After sellers have chosen the second-period prices, buyers are confronted with one

price per seller according to their first-period purchase and tracking decisions as

shown in Table 3.1.

Purchase

decision

Tracking

decision

Price of

seller A

Price of

seller B

Open data treatment

Seller A allow Loyalty price Poaching price

Seller A don’t allow New customer price New customer price

Seller B allow Poaching price Loyalty price

Seller B don’t allow New customer price New customer price

Exclusive data treatment

Seller A allow Loyalty price New customer price

Seller A don’t allow New customer price New customer price

Seller B allow New customer price Loyalty price

Seller B don’t allow New customer price New customer price

Table 3.1: Prices visible to buyers according to purchase and tracking decision.

Buyers then make their second-period purchase decision. After this, the sellers

receive full information about the buyers’ decisions. By this they also indirectly learn

about the buyers’ tracking decisions. This information is fully conclusive in case of

the open data treatment, as the total number of buyers that bought at the loyalty

or poaching prices corresponds to the total number of buyers that allow tracking.

In the exclusive data treatment, it serves as a lower bound, in the number of buyers

that bought at the loyalty prices. Those who bought at the new customer prices

may or may not have allowed tracking. When entering a new market round the

information of all past market rounds is accessible via a history box. While market

rounds are independent, the history of past rounds may serve sellers in forming their

3.3. EXPERIMENT

beliefs of the share of anonymous consumers.

At the end of a market round a seller receives the profit

Π = p1·n1+p2·n′

with p1corresponding to the chosen first-period price under which n1is the number

of buyers who bought from the seller. Similarly p2is the vector of the second-period

prices and n2the vector of the number of second-period buyers who bought from

the seller. Buyers have an induced reservation value of 15. The utility of a buyer

for a purchase32 is

Ut= 15 −pt−τ

with ptdescribing the price of the product that the buyer chose in period tand τ

describing the transportation costs. Profits and utilities are aggregated over all 20

market rounds, making every decision payment relevant.

Control measures

We complemented our market game by collecting several control measures. First,

we employed a novel single-player version of the Game of 21 Dufwenberg et al.

(2010) which we call the Game of 22. This task serves several purposes. We suspect

pricing decisions in this rather complex environment to be cognitively challenging

for subjects. Heterogeneity of the subjects can lead to different observations of

pricing behavior. We capture some of this heterogeneity in the capability of iterative

reasoning. Likewise, buyers’ first period purchasing and privacy choices may be

correlated with their ability to backward induct. A full description, instructions

and results of the Game of 22 are found in the Appendix.

Second, in an ensuing questionnaire, we ask participants to express their opinion

about privacy issues and whether they are concerned about privacy breaches. The

survey is based on Malhotra et al. (2004), which we use to calculate the Internet

Users’ Information Privacy Concerns (IUIPC) score. It consists of 10 statements,

to which participants answer on a 7-point Likert scale from “strongly agree” to

“strongly disagree”.33 Agreeing to the statement reflects a higher “privacy concern”.

The statements cover three broad categories: data collection, data control and data

usage. The IUIPC score is then calculated as the equally weighted average of the

average within-category scores normalized to [0,1]. We use the score as a rough

indication of the participants’ general stance towards privacy related issues.

32Within one market round a buyer makes four purchases. One per period per market.

33The full questionnaire is found in the Appendix.

3.3. EXPERIMENT

In the post-experimental questionnaire we additionally collected the participants

age, gender and field of study.

Procedure

In total 160 students participated, with 96 taking the role of a buyer and 64 taking

the role of a seller in the market game. For both treatments we formed eight indepen-

dent matching groups with six buyers and four sellers each. Both buyers’ utilities and

sellers’ profits from the market game are measured in ECU (Experimental Currency

Unit) and exchanged at the rate 10 ECU = 0,20 EUR. On average, subjects earned

about 20 EUR in the 90 minutes experiment. Most subjects were majors in eco-

nomics, mathematics or industrial engineering. 36 % of the subjects were female.

Participants earned 2 EUR when they won against the computer in the Game of 22,

which 91.25 % of the participants successfully did. Lastly, participants were awarded

1 EUR for filling out the privacy survey. Sessions were conducted in the laboratory

of TU Berlin and WZB in September and November 2019 with participants drawn

from the ORSEE pool (Greiner, 2015b). The experiment was programmed and

conducted with the experiment software z-Tree (Fischbacher, 2007b).

3.3.2 Hypotheses

We derive four qualitative hypotheses from our theoretical model. For our first hy-

pothesis we define second-period discounts as any difference between the first-period

price and a second-period price (loyalty, poaching or new customer price). Compar-

ing first- and second-period prices within data treatments following Propositions 1

and 3 we arrive at Hypothesis 1.

Hypothesis 1 We expect second-period discounts in the open data treatment, but

not in the exclusive data treatment.

We define poaching discounts as a (positive) difference between loyalty price and

poaching price.34 Note that sellers cannot set poaching prices in the exclusive data

treatment, but may “poach” by means of the new customer price. We only expect

poaching discounts in the open data treatment, because from the theoretical model,

we learned that sellers set lower poaching prices to induce customers who bought

from their competitor to switch.

34Similarly, we define loyalty discounts as a (positive) difference between new customer price

and loyalty price.

3.3. EXPERIMENT

Hypothesis 2 We expect poaching discounts in the open data treatment but not in

the exclusive data treatment.

From the theoretical analysis, we expect that all buyers reveal their information

in the open data treatment, while no buyer should reveal information in the ex-

clusive data treatment.35 When all buyers disclose their information, both data

treatments conform to behavior-based price discrimination. The opposite case, i.e.,

full anonymization, corresponds to uniform pricing. While full disclosure is always

better for buyers, the exclusive data treatment yields a coordination problem for

buyers, since every buyer has an incentive to anonymize.

Hypothesis 3 We expect more information disclosure in the open data treatment

compared to the exclusive data treatment.

In the following we define switching as any instance of buyers that purchase from

a different firm in period 2 than in period 1. Further, we define poaching as any

instance of switching when buyers switch from their nearest firm to their respective

farthest firm. This entails negative impacts on total welfare (cf. Section 3.2.3).

Likewise, we define retaining as any instance of switching where buyers shift from

the farthest to the nearest firm. This form of switching restores efficiency in terms

of total welfare. Given that our derived equilibria are symmetric we do not expect

any instances of retaining, which implies that every occurrence of switching should

follow our definition of poaching. In theory, we observed that welfare in the open

data treatment was lower than in the exclusive data treatment because of poaching.

Hypothesis 4 We expect more switching in the form poaching and lower total wel-

fare in the open data treatment compared to the exclusive data treatment.

3.3.3 Results

Seller and buyer decisions are mutually dependent. Therefore, we first briefly discuss

summary statistics concerning both buyers and sellers. Afterwards, in order of

action, we examine sellers pricing decisions and then buyers purchasing and privacy

decisions, including switching patterns and welfare implications.36

35Buyers bear a mass in the experiment due to the discretization. Lemmas 3 and 7 still apply.

Sellers would set the same price deviators would have paid others.

36While buyers actions dictate sellers beliefs, we assume those to be fixed when entering a new

market round. Likewise buyers beliefs about second period prices are fixed when entering a new

market round.

3.3. EXPERIMENT

Treatment Open data Exclusive data

First-period price

All 20 rounds 5.68 5.47

Last 10 rounds 5.55 5.54

Equilibrium prediction 8 6

Loyalty price

All 20 rounds 4.12 3.94

Last 10 rounds 3.97 4.07

Equilibrium prediction 4 6

New customer price

All 20 rounds 4.20 4.02

Last 10 rounds 3.85 3.79

Equilibrium prediction 4 6

Poaching price

All 20 rounds 3.28 n/a

Last 10 rounds 3.01 n/a

Equilibrium prediction 2 n/a

Table 3.2: Summary statistics for pricing choices of sellers.

Table 3.2 shows average prices of all 20 rounds and the last 10 rounds of the

experiment and the associated theoretical predictions.37 The inclusion of separate

statistics for the second half of the experiment accounts for learning and the contin-

uing formation of beliefs. First-period prices are substantially larger than second-

period prices in both treatments and overall somewhat higher in the open data

treatment compared to the exclusive data treatment. In the open data treatment

we observe poaching prices about one unit below loyalty and new customer prices,

while the latter two are relatively equal. This difference remains constant, while

overall prices are lower in the second half. In the exclusive data treatment we ob-

serve some poaching by means of the new customer prices, which are below loyalty

prices in the second half of the experiment.

We find buyers do not favor one seller over the other. In the open data treatment

(exclusive data treatment), 49.01% (51.25%) purchased from seller Ain the first

period and 49.69% (49.48%) purchased from seller Ain the second period.38 Buyers

rather predominantly purchase at the lowest total costs, where total costs are the

sum of the price and transportation costs. In the open data treatment (exclusive

data treatment), 97.29% (96.56%) of the first-period purchases and 97.34% (98.39%)

37The equilibrium predictions of the new customer price in the open data treatment and the

loyalty price in the exclusive data treatment are based on Lemmas 3 and 7.

38When restricting to the last 10 rounds all figures are closer to 50%

3.3. EXPERIMENT

Treatment Open data Exclusive data

Information disclosure

All 20 rounds 67.19% 65.36%

Last 10 rounds 66.77% 58.54%

Model prediction 100% 0%

Share of switching

All 20 rounds 23.18% 15.73%

Last 10 rounds 23.44% 17.40%

Model prediction 33.¯

3% 0%

Share of poaching

All 20 rounds 13.02% 7.50%

Last 10 rounds 13.02% 9.17%

Model prediction 33.¯

3% 0%

Share of retaining

All 20 rounds 10.16% 8.23%

Last 10 rounds 10.42% 8.23%

Model prediction 0% 0%

Table 3.3: Summary statistics for purchasing and privacy choices of buyers.

of the second-period purchases were made at the lowest total costs.39 As shown in

Table 3.3, the share of information disclosure is nearly equal for both treatments

at around 2/3. We find that the rate decreases for the second half in the exclusive

data treatment. Switching is more prevalent in the open data treatment compared

to the exclusive data treatment. However, we observe an increase in switching over

time in the exclusive data treatment which is driven by an increase in poaching, as

the share of retaining remains unaffected.

Going forward we express purchases in terms of the proximity to the closest

seller to account for the symmetry of the market environment. This allows us to

clearly distinguish switchers into two subgroups as defined for Hypothesis 4. We

consider those as poached who first purchase from their close seller and switch to

their far seller and those as retained who first purchase from their far seller and

switch to their close seller. While the former is detrimental to total welfare, the

latter restores welfare in inefficient first-period outcomes. In Table 3.3 we show that

there is considerable retaining in both treatments.

In Table 3.11 we show the order of purchases per buyer location. We observe that

the share of those who bought from the same seller twice decreases with increasing

distance from the seller. Switchers who purchased from different sellers between pe-

riods are more prevalent closer to the center, with highest occurrence at the central

39When restricting to the last 10 rounds all figures are closer to 100%.

3.3. EXPERIMENT

locations 4and 5. Further, we show the distribution of information disclosure in

Table 3.11. At first glance we find that information disclosure is largely independent

of locations in both treatments. Notably disclosure rates are slightly smaller (larger)

in the central locations in the open data treatment (exclusive data treatment). How-

ever, Pearson’s chi-squared tests neither reveal a significant difference from a uniform

distribution in the open data treatment, χ2(5, N = 1290) = 3.78, p = 0.58, nor in

the exclusive data treatment, χ2(5, N = 1255) = 2.57, p = 0.77.40

Sellers’ pricing decisions

First we investigate price setting of sellers within treatments as this is instrumental

to understand privacy and purchasing decisions of buyers. Throughout, we employ

random-effects regressions with subject-specific intercepts, clustered on group level.

First, we regress on respective price differences and analyze the constant remainder.

As shown in Table 3.4 we find significant differences between all second-period

prices compared to first-period prices. We expected this for the open data treatment,

but not for the exclusive data treatment according to Hypothesis 1. Predictions for

the exclusive data treatment are rested on the fact that buyers fully anonymize.

However, we observe a high rate of information sharing, which is consistent with

differences between first- and second-period prices. As a second-order effect this

should also lead to price discrimination, which we only observe towards the second

half as seen in the last column of Table 3.4.

There are significant differences between poaching price compared to loyalty and

new customer price in the open data treatment in line with part one of Hypothesis 2.

We find mixed results on the difference between new customer and loyalty prices

in both treatments. Initially, new customer prices are actually larger than loyalty

prices, which is indicated by the negative sign. Albeit this effect is insignificant, it

is also quite evident from Figures 3.23 and 3.24, where we see that loyalty discounts

were offered in the first 5 rounds. This shifts, as the significant second half dummy

indicates that sellers begin to adapt by employing poaching strategies in the exclusive

data treatment. In the open data treatment we observe an insignificant, but similar

tendency.

Next, we are interested in differences in price setting behavior between treat-

ments. We measure the effects on prices between treatments by random-effects re-

gressions with group-level clustering and control for demographics, iterative thinking

capability and learning effects.

40In Chapter 3.6 in the Appendix we explore how privacy concern affects disclosure rates for

some locations.

3.3. EXPERIMENT

Open data treatment Exclusive data treatment

pintro

−ployal

pintro

−pnew

pintro

−ppoach

ployal

−pnew

ployal

−ppoach

pnew

−ppoach

pintro

−ployal

pintro

−pnew

ployal

−pnew

Constant 1.50∗∗∗ 1.27∗∗∗ 2.25∗∗∗ -0.23 0.75∗∗∗ 0.98∗∗∗ 1.54∗∗∗ 1.14∗∗∗ -0.39

(0.227) (0.225) (0.071) (0.258) (0.227) (0.223) (0.207) (0.272) (0.286)

Second half 0.12 0.43∗0.30∗∗ 0.32 0.18 -0.13 -0.06 0.62∗∗ 0.68∗∗

(0.195) (0.226) (0.129) (0.237) (0.176) (0.248) (0.143) (0.273) (0.334)

Observations 640 640 640 640 640 640 640 640 640

Standard errors in parentheses. Estimation by fixed-effects regression. ∗,∗∗ and ∗∗∗ denote significance at the

10%, 5% and 1% level, respectively.

Table 3.4: Price differences within treatments.

In Table 3.5 we show the results. We find no significant effects on first-period,

loyalty and new customer prices. Though insignificant, the signs of all three effects

correspond to our theoretical predictions. Most notably there is a significant effect

on poaching prices, indicating that sellers poach more (intensively) in the open data

treatment. These results are in favor of Hypothesis 2.

We calculate the optimal average second-period prices under the observed share

of anonymous consumers and the observed number of first-period buyers according

to our derived reaction functions from Lemmas 1 and 2 to correct the predictions

of our model for the respective second-period sub-game under pooling beliefs. We

have shown earlier via chi-squared tests that the privacy choices over locations are

not significantly different from a uniform distribution, supporting the use of pooling

beliefs here.

In Table 3.6, we show the observed prices compared to the predictions when

adjusted for the observed first-period purchasing and privacy choices. In Figure 3.23

and Figure 3.24, we show how the observed and predicted prices develop over rounds.

We find that sellers adjusted loyalty and poaching prices in the open data treatment

First-period price New customer price Loyalty price Poaching price

(1) (2) (3) (4) (5) (6) (7) (8)

Exclusive -0.205 -0.021 -0.173 0.167 -0.153 0.162 0.741∗0.920∗

(0.442) (0.395) (0.503) (0.444) (0.423) (0.345) (0.446) (0.499)

Learning No Yes No Yes No Yes No Yes

Demographics No Yes No Yes No Yes No Yes

Cognitive ability No Yes No Yes No Yes No Yes

Observations 1280 1280 1280 1280 1280 1280 1280 1280

We use poaching price ≡new customer price in the exclusive data treatment. Standard errors in parentheses.

Estimation by random-effects regression with clustering on group level. ∗,∗∗ and ∗∗∗ denote significance at the

10%, 5% and 1% level, respectively.

Table 3.5: Price differences between treatments.

3.3. EXPERIMENT

Loyalty price New customer price Poaching price

Open data treatment

Observed average prices

All 20 rounds 4.20 4.12 3.28

Last 10 rounds 3.85 3.94 3.01

Model prediction

All 20 rounds 4.12 6 2.14

Last 10 rounds 4.13 6 2.11

Exclusive data treatment

Observed average prices

All 20 rounds 3.94 4.02 n/a

Last 10 rounds 4.07 3.79 n/a

Model prediction

All 20 rounds 4.55 3.10 n/a

Last 10 rounds 4.66 3.33 n/a

Table 3.6: Observed and adjusted price predictions under pooling assumption.

reasonably well. We find a striking discrepancy for the new customer price in the

open data treatment compared to the prediction. As we have shown in Table 3.4

sellers chose new customer prices relatively close to loyalty prices. This is reminiscent

of the off-path response of sellers to deviating buyers, which we lay out in Lemmas 3

and 7 in the Appendix. While this should lead to a ratchet effect on the loyalty and

poaching prices, which we do not observe, it might explain the sellers’ strategies. In

the exclusive data treatment, we see a similar but slowed down adjustment process

to the open data treatment for loyalty and poaching prices. Together with the

second-period discounts, this qualitatively fits the predictions from our model when

accounting for observed first-period purchases and privacy choices.

Buyers’ purchasing and privacy choices

Though buyers opted for the lowest total costs when purchasing, this does not

conclusively suggest myopic purchasing decisions. To account for strategic purchase

decisions we check what purchasing decisions buyers made when total costs were

equal.

As shown in Table 3.7, the share of buyers who purchase at the far seller when

total costs are equal increases towards the second half of the experiment and is am-

plified for those who allow purchase tracking in the open data treatment. The same

is not true for the exclusive data treatment, where the share is within 2 percentage

points around 35% under all conditions. As sellers offered loyalty discounts in the

3.3. EXPERIMENT

Open data Tracking

treatment allow don’t allow

First half 59.57% 43.48%

Second half 70.83% 55.17%

Exclusive data Tracking

treatment allow don’t allow

First half 36.84% 35.29%

Second half 35.59% 33.33%

Table 3.7: Share of purchases from the far seller at equal total costs.

initial rounds, it is sensible for buyers to stick with the close seller initially. Though

sellers refrained from offering loyalty discounts in the later rounds, buyers did not

adapt and were still more likely to choose the close seller when total costs were

equal. In Table 3.12 in the Appendix, we show that we can confirm a significant

treatment effect. Under equal total costs buyers were more likely to purchase from

the far seller in the open data treatment, suggesting strategic purchase decisions in

the first period.

0 5 10 15 20

Round

Open data treatment Exclusive data treatment

Figure 3.6: Fraction of buyers who share their data over rounds by treatment.

Upon first inspection in Figure 3.6, we observe two things regarding the purchase

tracking decision between treatments over rounds. Allowing tracking is initially

more and subsequently less prevalent in the exclusive data treatment compared

to the open data treatment. Albeit the similar sharing rate over all treatments,

this suggests that the adaptive processes are different between treatments. This

reflects the findings of Schudy and Utikal (2017) who show that subjects are less

inclined to share information, if more parties receive the information. Subjects in

our experiment face a similar situation, since there are two recipients in the open

data treatment and only one in the exclusive data treatment.

In Table 3.8, we explore this by employing a multi-level logit model on the track-

3.3. EXPERIMENT

ing decision of buyers, while controlling for demographics and experiment specific

factors, as well as, iterative thinking capability and privacy concern. Following spec-

ifications (1) and (2), we see no immediate treatment effect. In specifications (3) and

(4), we explore the role of learning, by including a dummy variable which indicates

the second half of the experiment, corresponding to rounds 11 and after, and an

interaction effect of treatment and second half dummy.41 There is a significant drop

in information disclosure in the exclusive data treatment, while there is no change

after learning in the open data treatment. We find some evidence towards Hypoth-

esis 3, when accounting for learning effects. We observe less information sharing in

the exclusive data treatment over time, though information sharing is much more

prevalent than predicted. This reflects the public good nature of information dis-

closure in the data environment.

Next, we take a closer look at the switching behavior of buyers. As discussed

earlier and shown in Table 3.11, we observe instances of poached and retained buy-

ers. In specification (1) of Table 3.9, we show that switching is significantly more

prevalent in the open data treatment. In specification (2), we show that this effect is

not merely driven by the treatment, but by those who disclose information. While

the effect is significant and positive in the open data treatment, we find a nega-

tive significant effect with nearly the same magnitude in the interaction with the

Tracking allowed ∈ {0,1}

(1) (2) (3) (4)

Exclusive 0.036 -0.017 0.442 0.388

(0.264) (0.253) (0.289) (0.280)

Second half -0.046 -0.046

(0.181) (0.180)

Exclusive ×Second half -0.763∗∗∗ -0.765∗∗∗

(0.282) (0.283)

Market No Yes No Yes

Location No Yes No Yes

Demographics No Yes No Yes

Privacy concern No Yes No Yes

Iterative thinking No Yes No Yes

Observations 3840 3800 3840 3800

Standard errors in parentheses. Estimation by random-effects logistic regression with clustering

on group level. ∗,∗∗ and ∗∗∗ denote significance at the 10%, 5% and 1% level, respectively.

Table 3.8: Impact of learning on tracking decision.

41Results are similar when using a continuous variable indicating the round instead of the

dummy for the second half.

3.3. EXPERIMENT

Switched ∈ {0,1}Poached ∈ {0,1}Retained ∈ {0,1}

(1) (2) (3) (4) (5) (6)

Exclusive -0.495∗∗∗ -0.052 -0.650∗∗∗ -0.016 -0.223 -0.064

(0.156) (0.172) (0.226) (0.226) (0.137) (0.220)

Tracking 0.590∗∗∗ 0.642∗∗∗ 0.247

(0.199) (0.191) (0.164)

Exclusive ×Tracking -0.594∗-0.756∗∗ -0.203

(0.318) (0.357) (0.271)

Market No Yes No Yes No Yes

Location No Yes No Yes No Yes

Demographics No Yes No Yes No Yes

Privacy concern No Yes No Yes No Yes

Iterative thinking No Yes No Yes No Yes

Observations 3840 3840 3840 3800 3840 3840

Standard errors in parentheses. Estimation by random-effects logistic regression with clustering on group level.

∗,∗∗ and ∗∗∗ denote significance at the 10%, 5% and 1% level, respectively.

Table 3.9: Effects of treatment and privacy choice on switching, poaching and retaining of buyers.

exclusive data treatment. This indicates that information disclosure is predictive

of switching in the open data treatment, but not in the exclusive data treatment.

We observe the same pattern in specifications (3) and (4) when limiting to those

instances of switching that follow our definition of poaching. In contrast, none of the

stated effects is found when limiting to retained buyers in specifications (5) and (6),

suggesting that this is neither driven by the treatment, nor by the privacy decisions.

Together, the results speak in favor of the first part of Hypothesis 4. We observe

significantly more switching, in the form of poaching, in the open data treatment

compared to the exclusive data treatment.

Welfare findings

In order to analyze the effect of switching on welfare, we use transportation costs as

an inverse measure for welfare. Figure 3.7 depicts predicted and observed average

transportation costs for both treatments.

min max

44.

Predicted

4.375 4.515

Observed Exclusive data

Open data

Figure 3.7: Observed and predicted average transportation costs per round.

3.3. EXPERIMENT

The left and right boundaries of the line give the average minimal and maximal

transportation costs per market round (i.e., two periods). This implies that the

left boundary corresponds to the maximum welfare. Four are the lowest average

transportation costs per round if buyers purchase from the closest seller. This is also

the predicted value for average transportation costs in the exclusive data treatment

because we expect all buyers to anonymize and buy from the closest seller in both

periods. The predicted average transportation costs for the open data treatment

are 4.¯

3because we expect all buyers to share information and a portion of 1

3to

switch to the far seller in the second period (cf. Table 3.3). Underneath the line, we

depict the observed average transportation costs across treatments. The exclusive

data treatment’s observed average transportation costs are 4.375. The open data

treatment’s observed average transportation costs are 4.515. Although both values

are close to the maximum welfare of four, they are above the prediction of the open

data treatment of 4.¯

Buyer’s transportation

costs in both periods

Buyer’s transportation

costs in the first period

Buyer’s transportation

costs in the second period

(1) (2) (3) (4) (5) (6)

Exclusive -0.143 -0.153 -0.003 -0.010 -0.140∗∗ -0.143∗∗

(0.106) (0.103) (0.050) (0.050) (0.070) (0.064)

Second half -0.082 -0.082 -0.020 -0.020 -0.063 -0.062

(0.052) (0.052) (0.027) (0.027) (0.041) (0.041)

Exclusive ×Second half 0.005 0.005 -0.049 -0.049 0.054 0.054

(0.093) (0.094) (0.059) (0.059) (0.052) (0.052)

Market No Yes No Yes No Yes

Demographics No Yes No Yes No Yes

Privacy concern No Yes No Yes No Yes

Iterative thinking No Yes No Yes No Yes

Observations 3840 3840 3840 3840 3840 3840

Standard errors in parentheses. Estimation by random-effects regression with clustering on group level. ∗,∗∗ and

∗∗∗ denote significance at the 10%, 5% and 1% level, respectively.

Table 3.10: Effects of treatment on buyer’s transportation costs in first, second and both periods.

In Table 3.10, we show the results of random-effects regressions on the buyer’s

per-period transportation costs on a subject level. Specifications (1) and (2) show

that the overall welfare effect is insignificant. Via specifications (3) and (4), we

show that there is no effect on the transportation costs in the first period, while

specifications (5) and (6) reveal an effect for the second period. In line with the

observation that more buyers switch inefficiently in the open data treatment, we

observe lower second period transportation costs in the exclusive data treatment.

This finding is in line with the second part of Hypothesis 4. It also shows that the

observed difference in transportation costs is solely driven by the second period,

where we observed more poaching in the open data treatment.

3.4. CONCLUSION AND DISCUSSION

3.4 Conclusion and Discussion

In this article, we analyze consumers’ endogenous privacy decisions in a duopolistic,

dynamic market where firms employ behavior-based price discrimination. We con-

sider two data policies, distinct in the number of firms that can access consumers’

data, containing their purchase history. In the open data policy, data disclosed by

consumers are fully shared between firms, whereas in the exclusive data blue, data

are only available to the provider of the good.

In our theoretical analysis, we find a unique pure-strategy equilibrium for each

data policy. When information is available to both firms, all consumers fully disclose

their data, which amplifies competition. Second-period prices are below first-period

prices and firms offer poaching discounts. When information is exclusive to suppliers

of the good, all consumers hide their data because they are individually better off

by anonymizing. Consequently, second-period and first-period prices correspond

to uniform pricing. While consumers’ data sharing is favorable under both data

policies, there is only an incentive to do so under the open data policies, but not

under the exclusive data policy. The exclusive data policy exhibits information

externalities where a collective choice of full information disclosure would lead to

a better outcome for consumers, but individually consumers refrain from sharing

information. This is also reflected in consumer’s welfare which suffers under an

exclusive data policy and is higher under an open data policy due to poaching

discounts. For firms, profits are higher under the exclusive data policy. Social

welfare is maximal under the exclusive data policy because in the absence of poaching

discounts there is no inefficient switching.

In order to verify our theoretical results, we conduct a laboratory experiment

that is aligned with our theoretical model where subjects act in the roles of sellers

and buyers. We develop two treatments that correspond to the two data policies. We

find that the data sharing rate under the open data policy is high which is in line with

our theory. The data sharing rate in the exclusive treatment is significantly lower

compared to the rate in the open data treatment when factoring in a learning process.

Sellers act largely in accordance with our theory in the open data treatment. They

price discriminate on the basis of data they receive by offering poaching discounts.

In the exclusive data treatment, sellers initially do not offer discounts to anonymous

buyers even though they have access to necessary information. Over time sellers

in the exclusive treatment begin to adopt poaching strategies and in turn buyers

refrain from disclosing information, which is in line with our predictions.

The theoretical welfare results hinge on the unique pooling equilibria. That

social welfare is higher under an exclusive data policy is solely driven by the fact

3.4. CONCLUSION AND DISCUSSION

that there is no inefficient switching. However, we cannot confirm this social welfare

effect in our experiment. Though we can confirm increased switching in the open

data treatment over the exclusive data treatment, we find no significant difference

in social welfare across treatments. In our analyses, the difference between open

data and exclusive data policy shows that mandated data sharing among firms

will lead more consumers to share data because they can benefit from intensified

competition. Whereas under an exclusive data policy, firms can use consumers’ data

to price discriminate without the pressure of increased competition because firms

operate under asymmetric information.

In future research, we are interested in extending our model by including more

general beliefs for consumers’ privacy choice. We expect that the proof of the unique

equilibria we find also holds for more general beliefs such that the equilibria are not

restricted to pure strategies anymore. Another interesting aspect is extending our

model by a setting where consumers have complete control over their data. Complete

control entails that consumers can decide whether each firm independently receives

data about their previous purchases. This way, consumers can also exclusively share

their purchasing history with firms that they have not bought from. Basically, this

extends our open data policy by allowing consumers to choose a different option

for each firm. Along this line, one can also imagine a situation of asymmetric

information, i.e., a small retailer unable to collect and process consumers’ data

versus a large retailer accessing a wide range of personal data.

Two more research questions come to mind on basis of our theoretical and exper-

imental findings First, It would be interesting to further study consumers’ concern

for their privacy in the specific e-commerce setting and the drivers of their privacy

decision to determine on what basis consumers decide to share or hide their data.

Second, it is equally important to explore firms’ perspective and study under which

conditions they have an incentive to share obtained data with other firms. We did

not include this option in our model as our open data policy implies mandated data

sharing, while under the exclusive data policy this possibility was not given at all.

3.5. APPENDIX – THEORETICAL PART

3.5 Appendix – Theoretical Part

Proof of Lemma 1

The marginal consumer on the anonymous line is determined by v−pA

2−θ2=v−pB

2−(¯

θ−θ2)

as θ2=¯

2+pB

2−pA

2.The marginal consumers on the line of recognized consumers are

characterized by v−pA

2,A −θA

2=v−pB

2,A −(¯

θ−θA

2), which is equivalent to

θA

2=¯

2+pB

2,A −pA

2,A

and accordingly, on B’s turf θB

2is determined by

θB

2=¯

2+pB

2,B −pA

2,B

The maximization problem of the firms concerning the anonymous consumers is given by

max

λpA

2[¯

2+pB

2−pA

2],

max

λpB

2[¯

θ−(¯

2+pB

2−pA

2)].

Firms’ maximization problems for anonymous consumers give the first-order conditions

2+pB

2−pA

2= 0,¯

2−pB

2+pA

2= 0.

From these we derive prices pA

2=pB

2=¯

θand the marginal consumer, θ2=¯

Among the recognized consumers we have the following maximization problems:

max

2,A,pA

2,B

(1 −λ)[pA

2,AθA

2+pA

2,B(θB

2−θ1)],

max

2,B,pB

2,A

(1 −λ)[pB

2,B(¯

θ−θB

2) + pB

2,A(θ1−θA

2)].

By plugging θA

2=¯

2+pB

2,A−pA

2,A

2and θB

2=¯

2+pB

2,B−pA

2,B

2into the maximization problems,

we get

max

2,A,pA

2,B

(1 −λ)[pA

2,A(¯

2+pB

2,A −pA

2,A

2) + pA

2,B(¯

2+pB

2,B −pA

2,B

2−θ1)],

max

2,B,pB

2,A

(1 −λ)[pB

2,B(¯

θ−¯

2−pB

2,B −pA

2,B

2) + pB

2,A(θ1−¯

2−pB

2,A −pA

2,A

2)].

3.5. APPENDIX – THEORETICAL PART

First-order conditions solve

(1 −λ)[¯

2+pB

2,A

2−pA

2,A]= 0,

(1 −λ)[¯

2+pB

2,B

2−pA

2,B −θ1]= 0,

(1 −λ)[¯

2−pB

2,B +pA

2,B

2] = 0,

(1 −λ)[θ1−¯

2−pB

2,A +pA

2,A

2] = 0,

where we can derive the results as

2=¯

θ, pA

2,A =1

3(2θ1+¯

θ), pA

2,B =1

3(3¯

θ−4θ1),

2=¯

θ, pB

2,B =1

3(3¯

θ−2θ1), pB

2,A =1

3(4θ1−¯

θ).

From these equations we observe that anonymous prices pA

2and pB

2are strictly positive, the

same for loyalty prices pA

2,A and pB

2,B. However, poaching prices pA

2,B and pB

2,A depend on

θ1and the parameter ¯

θ. When 1

4¯

θ≤θ1≤3

4¯

θ, it is an interior solution and the equilibrium

prices are just as above. When θ1<1

4¯

θ, it is a corner solution where pB

2,A = 0. Firm A

should set pA

2,A such that v−pA

2,A −θ1=v−(¯

θ−θ1), in order to protect the marginal

customer located at θ1. Therefore pA

2,A =¯

θ−2θ1and the other pirces are the same as in

the interior solution. When θ1>3

4¯

θit follows that pA

2,B = 0, and thereby firm B sets pB

2,B

such that v−θ1=v−pB

2,B −(¯

θ−θ1). So in this case pB

2,B = 2θ1−¯

θand the other prices

do not change.

Proof of Proposition 1

The first-period marginal consumer on the line of anonymous consumers is determined

by ˆ

θ1=¯

2+1

2(pB

1−pA

1). The first-period marginal consumer on the line of recognizable

consumers is defined by the following equivalence,

v−pA

1−θ1+[v−pB

2,A −(¯

θ−θ1)]=v−pB

1−(¯

θ−θ1) + [v−pA

2,B −θ1].

Hence, the marginal consumer is given by θ1=¯

2+3

8(pB

1−pA

1). Firm A’s problem is to

maximize the following term with respect to the first-period prices:

πA=λpA

1ˆ

θ1+ (1 −λ)pA

1θ1+λpA

2θ2+ (1 −λ)[pA

2,AθA

2+pA

2,B(θB

2−θ1)].

Similarly, firm Bmaximizes

πB=λpB

1(¯

θ−ˆ

θ1)+(1−λ)pB

1(¯

θ−θ1)+λpB

2(¯

θ−θ2)+(1−λ)[pB

2,A(θ1−θA

2) + pB

2,B(¯

θ−θB

2)].

3.5. APPENDIX – THEORETICAL PART

By inserting pA

2,A,pB

2,A,pA

2,B,pB

2,B, and θ1into firms’ maximization problems in the first

period, we can derive the fiirst-order conditions for Aand B, respectively,

2+3 + λ

8pB

1−3 + λ

4pA

1−5

16(1 −λ)(pB

1−pA

1)=0,

2+3 + λ

8pA

1−3 + λ

4pB

1+5

16(1 −λ)(pB

1−pA

1)=0,

which gives us firms’ prices for both periods.

When all consumers reveal their information, beliefs about anonymous consumers gov-

ern off-path behavior. If a single consumer individually deviates, both firms are driven to

a situation of perfect competition for this single consumer, which grants the highest rent

possible. Considering that both firms perfectly compete and denote ˜u(θ)as the utility of

a consumer of type θwho deviates:

˜u(θ)42 =⎧

⎪

⎨

⎪

⎩

v−¯

θ+θif θ≤¯

v−θif θ≥¯

From firms’ perspective, their belief about who may deviate depends on the utilities a

consumer gets with and without deviation. Based on the optimal pricing strategy from

Proposition 1 and the utility with deviation ˜u(θ)derived above, we check six cases sepa-

rately: when 0≤θ≤¯

6, the utility of a consumer of type θwithout deviation is v−2

3¯

θ−θ,

which is larger or equal to the utility ˜u(θ)if they deviate, that is v−¯

θ+θ. When ¯

6< θ ≤¯

the utility of a consumer of type θwithout deviation is again v−2

3¯

θ−θ, which is strictly

smaller than the utility if they deviate, that is v−¯

θ+θ. When ¯

3< θ ≤¯

2, the utility of

a consumer of type θwithout deviation becomes v−1

3¯

θ−(¯

θ−θ), which is smaller than

the utility ˜u(θ)if they deviate, that is v−¯

θ+θ. Similarly, when ¯

2< θ ≤2

3¯

θ, the utility

of a consumer without deviation changes to v−1

3¯

θ−θ, which is smaller than the utility

with deviation, equivalent to v−θ. When 2

3¯

θ < θ < 5

6¯

θ, the utility of a consumer without

deviation is v−2

3¯

θ−(¯

θ−θ), which is smaller than the utility with deviation v−θ. Finally,

when 5

6¯

θ≤θ≤¯

θ, the utility of a consumer without deviation is again v−2

3¯

θ−(¯

θ−θ),

which is larger or equal to the utility with deviation v−θ. Overall, we get that consumers

located between 1

6¯

θand 5

6¯

θmay have an incentive to deviate, thus firms form their off-

path belief accordingly. Figure 3.8 depicts the total costs v−˜u(θ)for consumers under

individual deviation, given the sellers’ responses.

Lemma 3 If firms observe a deviation of consumers’ privacy choice, they believe with

equal probability that it is any consumer located at θ∈(1

6¯

θ, 5

6¯

θ). The off-path price for

this segment is 2

3¯

θ.

42In the perfect competition, the firm further away from the deviating consumer would set the

price at zero and this consumer would be indifferent between buying from either firm.

3.5. APPENDIX – THEORETICAL PART

θ1

θ2

θ5

Potential deviators

Figure 3.8: Total costs in equilibrium (solid) and for individual deviators (dotted).

Since they cannot identify the exact type of the consumer who deviates, their belief is that

the consumer with an incentive to deviate is uniformly distributed between 1

6¯

θand 5

6¯

θ.

Therefore as a best response, they set the optimal off-path price 2

3¯

θ43 if they observe a

deviation. This price is equivalent to the optimal loyalty price derived in Proposition 1.

Under these beliefs no consumer anonymizes because the total costs are not lower than

under revealing information. Therefore, there is no profitable deviation for any consumer,

which completes the proof.

Proof of Proposition 2

In this section, we prove the non-existence of a separating equilibrium in pure strategies

under open data and thereby confirm the uniqueness of the pooling equilibrium derived in

Proposition 2.

We divide all the potential scenarios into two cases: (i) when the first-period cut-off

goes through a “hide” segment44 and (ii) when the first-period cut-off goes through a “give”

segment.45 We differentiate separating equilibria according to whether the line consists of

two segments or of mutiple segments. For instance, the Figure 3.9 shows the scenario of

multiple segments when the first-period cut-off goes through a “hide” segment.

θ′

0¯

give hide give

first-period cut-off

Figure 3.9: Line with multiple segments in case (i).

43Considering this off-path price, two firms face a continuum of consumers uniformly distributed

between 1

6¯

θand 5

6¯

θ, thus they choose ˜pA

2and ˜pB

2to maximize their respective profits ˜pA

2(¯

2+˜pB

2−˜pA

2−

6)and ˜pB

2[5

6¯

θ−(¯

2+˜pB

2−˜pA

2)], where we get that ˜pA

2= ˜pB

2=2

3¯

θ.

44I.e., to the left of the cut-off all the consumers bought from Firm A in the first period and to

the right all bought from Firm B.

45Please note that no assumption about symmetry is needed.

3.5. APPENDIX – THEORETICAL PART

Definition: If not all consumers within one segment buy from the same firm, we say that

there exists Poaching Behavior in this segment.

Lemma 4 In a separating equilibrium with multiple segments, there exists no poaching

behavior in any segment except for the segment that the first-period cut-off goes through,

i.e., there is no poaching behavior in a lateral segment.

Proof. We take the figure above as an example and use a proof by contradiction here.

Assume Lemma 4 is not true and there exists poaching behavior in the left “give” segment,

which means that to the left of θ′consumers buy from firm B at pB

2,A and to the right

of θ′consumers buy from firm A at pA

2. Since the consumer located at θ′is indifferent

between revealing and hiding information, the costs of two options should be the same for

them, i.e., pB

2,A + (¯

θ−θ′) = pA

2+θ′. However, for those who are located to the left of

θ′and buy from Firm B at pB

2,A, they have an incentive to deviate. That is because by

deviating to hide data, the total cost of buying from firm A would be strictly smaller than

the cost before.46 Thus, there exists a profitable deviation, which contradicts our initial

assumption. The same method can be applied to a “hide” segment. This completes the

proof.

Lemma 4 shows that in a separating equilibrium with multiple segments there is no poach-

ing behavior in lateral segments. Based on cut-offs between the lateral segments we can

infer that pi

2=pi

2,i ∀i=A, B. Now, we start to prove the non-existence of a separating

equilibrium in pure strategies.

As mentioned before, we have to look at case (i) and (ii) and in each case differentiate

by the number of segments (two or multiple). In other words, we need to check four possible

scenarios. Let’s first focus on the figure above, where there are multiple segments in case

(i). If we check the consumer located at θ′, they are indifferent between revealing and

hiding information. By Lemma 4, there is no poaching behavior in the “give” segments, so

2,A =pA

2. Similarly, pB

2,B =pB

2also holds. However, under such circumstances both firm

A and firm B have an incentive to deviate from their pricing strategy. By increasing their

loyalty prices when the consumers are segmented as in the figure above, both firms could

gain profit from loyal customers while keeping the profit from anonymous customers the

same as before. Thus, firms have a profitable deviation and such a separating equilibrium

does not exist.

Then we look at the scenario with just two segments in case (i). The Figure 3.10 below

describes such a scenario:

46Assume that they are located at θ′′ with θ′′ < θ′. Since they buy from firm B at pB

2,A, the

initial costs are pB

2,A + (¯

θ−θ′′), which is strictly larger than pB

2,A + (¯

θ−θ′). By deviating to hide

data, the total costs would be pA

2+θ′′, which is strictly smaller than pA

2+θ′. Combining together

we can get that pA

2+θ′′ < pA

2+θ′=pB

2,A + (¯

θ−θ′)< pB

2,A + (¯

θ−θ′′), which shows the benefit

from deviation.

3.5. APPENDIX – THEORETICAL PART

0¯

give hide

first-period cut-off

Figure 3.10: Line with two segments in case (i).

Firstly, we can show that in the “hide” segment there exists poaching behavior. Otherwise,

one of the firm’s new customer prices should be 0, since both pA

2and pB

2are exclusively

used in the “hide” segment and the firms have no reason to set a price above zero if they

get no market share in this interval. If this were the case, the customers from the “give”

segment would deviate to hide their data, since by doing so they could benefit from the

zero new customer price. Secondly, similar to Lemma 4 we can prove that in the “give”

segment no poaching behavior exists. In other words, all consumers buy from firm A at

2,A, and pA

2,A =pA

2. However, firm A has an incentive to raise their loyalty price, in

order to obtain more from loyal customers who shared their data. Thus, this structure of

separating equilibrium is not possible. Combining these two scenarios, we can conclude

that in case (i) (when the first-period cut-off goes through the "hide" segment) there is no

separating equilibrium in pure strategies.

0¯

hide give hide

first-period cut-off

Figure 3.11: Line with multiple segments in case (ii).

In case (ii) when the first-period cut-off goes through the “give” segment, let’s first look

at the scenario with multiple segments along the line. In Figure 3.11 above, by Lemma 4,

there is no poaching behavior in all “hide” segments. This means that in the left “hide”

segments firm A serves all customers at a price of pA

2and in the right “hide” segments

firm B serves all at a price of pB

2. It is similar for all “give” segments on the sides, such

that pA

2=pA

2,A and pB

2=pB

2,B. Under such circumstances both firms have an incentive

to increase their new customer prices pA

2and pB

2because this leads to a higher profit for

“hide” segments while keeping “give” segments the same as before.47 Hence, there is no

separating equilibrium in pure strategies in this scenario.

Finally, we check the scenario with just two segments. Considering the interval between θ′

and the first-period cut-off in Figure 3.12, there should exist poaching behavior. Otherwise,

47This situation is similar to a Hotelling line with discontinuous demands proposed by Ackley

(1942) and Shilony (1977).

3.5. APPENDIX – THEORETICAL PART

θ′

0¯

hide give

first-period cut-off

Figure 3.12: Line with two segments in case (ii).

by the same logic mentioned before, either pA

2,A or pB

2,A48 is zero, and some outside customers

deviate. Then similar to Lemma 4, we can easily show that no poaching behavior exists

in the “hide” segment and all customers buy from firm A at pA

2. In this condition firm A

has an incentive to increase the new customer price, in order to get more profit from the

“hide” segment. To sum it up, we prove that there is no separating equilibrium in pure

strategies in case (ii) when the first-period cut-off goes through the “give” segment.

All the analyses above show that there is no separating equilibrium in pure strategies

under the open data policy, which completes the proof of Proposition 2.

Open Data with Myopic Consumers

In the main analysis we consider consumers to be strategic. Now we want to extend our

analysis to a situation in which some consumers are myopic in the first stage with regard

to their purchasing decision (Baye and Sapi, 2014; Carroni et al., 2015). We assume that

there is a share αof myopic consumers and a share 1−αof strategic consumers. For

myopic consumers, their rationale is to choose the cheaper good in the first stage, however,

they are strategic afterwards, including the privacy choice and the purchasing decision in

the second stage. To the contrary, strategic consumers are always forward-looking in both

stages. Therefore, the difference in this setting lies in the first stage, where, among myopic

consumers, marginal consumer θ′

1is just indifferent between buying from firm Aat pA

1in

stage 1 and buying from firm Bat pB

1in stage 1, that is, v−pA

1−θ′

1=v−pB

1−(¯

θ−θ′

1),

leading to θ′

1=¯

2+pB

1−pA

2. On the other hand, among strategic consumers,49 the cut-off

consumer θ1is indifferent between buying from firm Aat pA

1in stage 1and then buying

from firm Bat pB

2,A in stage 2, and buying from firm Bat pB

1in stage 1and then buying

from firm Aat pA

2,B in stage 2,50 therefore,

v−pA

1−θ1+[v−pB

2,A −(¯

θ−θ1)]=v−pB

1−(¯

θ−θ1) + [v−pA

2,B −θ1].

In order to solve this two-stage problem we apply backward induction. Starting from the

48This interval represents those who bought from Firm A in the first stage and shared their

data. Therefore, they are facing the loyalty price pA

2,A and poaching price pB

2,A.

49To make it more precise, strategic consumers mean those who are forward-looking and reveal

their data in the first stage.

50This indifference condition is the same as under open data with strategic consumers.

3.5. APPENDIX – THEORETICAL PART

second stage, again there are two separated lines for consumers who did and who did

not share their data, respectively. No matter whether they belong to the group of myopic

consumers or the group of strategic consumers, the cut-offs are the same, since even myopic

consumers are strategic in the second stage. Among those who shared their data in the

first stage, the two cut-offs, θA

2and θB

2, are equivalent to ¯

2+pB

2,A−pA

2,A

2and ¯

2+pB

2,B−pA

2,B

respectively.51 Moreover, for those who did not share their data in the first stage, as we

discussed before, they will face uniform pricing in the second stage, with pA

2=pB

2=¯

θand

θ2=¯

Therefore, the competitors maximize their profits from the line with mass 1−λas

follows

max

2,A,pA

2,B

α(1 −λ)[pA

2,AθA

2+pA

2,B(θB

2−θ′

1)]+ (1 −α)(1 −λ)[pA

2,AθA

2+pA

2,B(θB

2−θ1)],

max

2,B,pB

2,A

α(1 −λ)[pB

2,B(¯

θ−θB

2) + pB

2,A(θ′

1−θA

2)]+ (1 −α)(1 −λ)[pB

2,B(¯

θ−θB

2) + pB

2,A(θ1−θA

2)].

Lemma 5 Combining these two optimization problems and deriving the first order condi-

tions, we obtain the following prices in the second stage

2,A =¯

3+2

3θ1+2

3α(θ′

1−θ1), pA

2,B =¯

θ−4

3θ1+4

3α(θ1−θ′

1),

2,B =¯

θ−2

3θ1+2

3α(θ1−θ′

1), pB

2,A =−¯

3+4

3θ1+4

3α(θ′

1−θ1).

Note that on the line with consumer mass λnothing changes and therefore the prices

correspond to uniform pricing.

On the first stage, the cut-offs are different among the myopic consumers and strategic

consumers, and also depend on their respective privacy choice. Therefore, there are four

groups of different consumers. Among the mass of λconsumers who do not share their

information, a mass of αλ are myopic and a mass of (1 −α)λare strategic. However, no

matter whether they are myopic or strategic, the cut-offs they face are the same, that is

θ′

1=¯

2+pB

1−pA

2.52 Similarly, among the mass of 1−λconsumers, there are α(1−λ)myopic

consumers facing the cut-off of θ′

1, while a mass of (1 −α)(1 −λ)are strategic consumers

with the cut-off of θ1.

Combining these indifference conditions and the results from Lemma 5, we obtain

θ′

1=¯

2+pB

1−pA

2and θ1=¯

2−4α−3

8(1−α)(pB

1−pA

1). Maximizing the overall profits in the

first period with respect to the first-stage prices, the two firms have the resulting objective

functions:

51The method to derive these cut-offs are identical to the open data policy with strategic

consumers.

52θ′

1will not be influenced by the prices in the second stage, which is similar to the open data

policy with strategic consumers.

3.5. APPENDIX – THEORETICAL PART

πA=α[λpA

1θ′

1+ (1 −λ)pA

1θ′

1+λpA

2θ2+ (1 −λ)pA

2,AθA

2+ (1 −λ)pA

2,B(θB

2−θ′

1)]

+ (1 −α)[λpA

1θ′

1+ (1 −λ)pA

1θ1+λpA

2θ2+ (1 −λ)pA

2,AθA

2+ (1 −λ)pA

2,B(θB

2−θ1)],

πB=α[λpB

1(¯

θ−θ′

1) + (1 −λ)pB

1(¯

θ−θ′

1) + λpB

2(¯

θ−θ2) + (1 −λ)pB

2,B(¯

θ−θB

2) + (1 −λ)pB

2,A(θ′

1−θA

2)]

+ (1 −α)[λpB

1(¯

θ−θ′

1) + (1 −λ)pB

1(¯

θ−θ1) + λpB

2(¯

θ−θ2)

+ (1 −λ)pB

2,B(¯

θ−θB

2) + (1 −λ)pB

2,A(θ1−θA

2)].

Lemma 6 Substituting the respective prices into the system of equations given by the first-

order conditions, we derive the final results for the first- and second-stage prices:

1=pB

1=4

3 + λ¯

θ,

2,A =pB

2,B =2

3¯

θ,

2,B =pB

2,A =1

3¯

θ,

2=pB

2=¯

θ.

Everyone shares their data, therefore the optimal λis 0and the resulting prices are identical

to the open data policy with strategic consumers.

The result above is a robustness check, showing that being strategic or myopic in the

first period purchase does not affect any decisions. Consumers choose to share their data

with firms, in order to benefit from competition; while firms use standard behavior-based

price discrimination to maximize their profits. Moreover, the strategic privacy choice is

sufficient to yield identical results including first period prices. This is not the case in

standard behavior-based pricing models without the privacy choice.

Open Data with Quadratic Transportation Costs

In this variation of the model, the utility for a consumer located at θis either v−pi−θ2if

buying from firm A, or v−pj−(¯

θ−θ)2if buying from firm B. As in the standard model,

we employ backward induction and finally find that pA

1=pB

1=4

3+λ¯

θ2, and θ1=1

2¯

θ,

2,A =pB

2,B =2

3¯

θ2,pA

2,B =pB

2,A =1

3¯

θ2. If the cost is quadratic in the standard behavior-

based pricing model, prices in the first stage are pA

1=pB

1=4

3¯

θ2, and the uniform pricing

strategy is pA

1=pB

1=¯

θ2. Prices reflect quadratic transportation costs. Thus, each buyer

shares their data, λ= 0, in order to get the lower price in the second stage and thus all

the results under the open data policy hold with quadratic transportation costs.

3.5. APPENDIX – THEORETICAL PART

Proof of Lemma 2

The maximization problems of the firms in the second period are given by:

max

2,pA

2,A

πA

2= max

2,pA

2,A

λpA

2θ2+ (1 −λ)pA

2,AθA′

2+ (1 −λ)pA

2(θB′

2−θ1),

max

2,pB

2,B

πB

2= max

2,pB

2,B

λpB

2(¯

θ−θ2) + (1 −λ)pB

2,B(¯

θ−θB′

2) + (1 −λ)pB

2(θ1−θA′

2).

When maximizing the profit functions of the second stage, we get the following expressions

for the first-order conditions:

∂πA

∂pA

=λ

2(pB

2−2pA

2+¯

θ) + (1 −λ)

2(pB

2,B −2pA

2+¯

θ)−(1 −λ)¯

θ= 0,

∂πA

∂pA

2,A

=(1 −λ)

2(pB

2−2pA

2,A +¯

θ)=0,

∂πB

∂pB

=λ

2(−2pB

2+pA

2+¯

θ) + (1 −λ)

2(−2pB

2+pA

2,A −¯

θ+ 2θ1)=0,

∂πB

∂pB

2,B

=(1 −λ)

2(−2pB

2,B +pA

2+¯

θ)=0.

This gives a system of equations, where prices are dependent on each other and need to be

substituted into each other in order to receive the final set of prices of the second period

that are only depending on λ,pA

1and pB

2,A(pB

2) = ¯

θ+pB

2(pB

2) = (3 −λ)¯

θ+ 2λ·pB

2−4(1 −λ)θ1

3 + λ,

2,B(pA

2) = ¯

θ+pA

2(pA

2) = −(1 −3λ)¯

θ+ 2λ·pA

2+ 4(1 −λ)θ1

3 + λ.

Note that unlike in Lemma 1 we do not need to consider the corner solution here. Under

the open data policy, the poaching price from one firm may be zero, but under the exclusive

data policy, firms cannot poach directly, but have use the new customer price instead. For

any firm i, setting the price pi

2at zero is a weakly dominated strategy since its marginal

cost is just zero. However, when the information is exclusive, the new customer price is

also applied to those who do not share their data. Considering the firm iagain, if the new

customer price from another firm pj

2is not zero, they always have an incentive to set the

price above zero in order to earn profits from those who hide their data, which will make

them strictly better off than choosing the corner solution. Thus, we do not consider the

corner solution under the exclusive data policy. All the equations above can easily derive

the results in Lemma 2.

3.5. APPENDIX – THEORETICAL PART

Proof of Proposition 3

In the case where all consumers hide their information, the counterfactual of consumers

who disclose information is governed by off-path beliefs. Suppose, without loss of gener-

ality, a single (atom-less) consumer who bought from Ain period 1 deviates by disclosing

information. The price setting of firm Bremains unchanged, since Bcannot target the

deviating consumer and the impact on the price is negligible. This consumer who identifies

towards Acan only be located on [0, θ1]and will receive a price from firm Ato make them

indifferent between buying from firm Aand firm B. Thus, the utility ˜u(θ)of a consumer

of type θwho deviates is:

˜u(θ)53 =⎧

⎪

⎨

⎪

⎩

v−2¯

θ+θif θ≤¯

v−¯

θ−θif θ≥¯

From the firm’s side, their belief about who may deviate depends on the utilities that the

consumer get with and without deviating. By Proposition 3 and the utility with deviation

˜u(θ)derived above, we check different scenarios separately: when 0≤θ < ¯

2, the utility of

a consumer of type θwithout deviation is v−¯

θ−θ, which is strictly larger than the utility

˜u(θ)if they deviate, that is v−2¯

θ+θ. When ¯

2< θ ≤¯

θ, the utility of a consumer of type

θwithout deviation is v−¯

θ−(¯

θ−θ), which is strictly larger than the utility ˜u(θ)if they

deviate, that is v−¯

θ+θ. Only when θ=¯

2, the utility of a consumer of type θdoes not

change with or without the deviation, as shown in Figure 3.13 at hands of the total costs

v−˜u(θ).

2¯

Potential deviator

Figure 3.13: Total costs in equilibrium (solid) and for individual deviators (dotted).

Lemma 7 If firms observe any deviation from consumers, they form the off-path belief

that it is the consumer located at ¯

2and set the off-path price ¯

θas a best response.

53Please note the firm that the deviating consumer did not buy from in the first stage sets the

price at ¯

θand this consumer is indifferent between buying from either firm.

3.5. APPENDIX – THEORETICAL PART

Since only the consumer in the center of the line gets the same utility from deviating, firms’

best response is to set the uniform price ¯

θ. However, consumers do not benefit from the

deviation, since the utility does not change. Therefore, the proof is complete.

Proof of Proposition 4

In this section, we look at the exclusive data policy, where similar arguments compared to

the proof of Proposition 2 are applied to prove that there is no separating equilibrium in

pure strategies. To do so we first expand Lemma 4 to the case of exclusive data.

Lemma 8 If there exists a separating equilibrium for a line with multiple segments under

exclusive data, there is no poaching behavior in the lateral segments.

θ′

0¯

give hide give

first-period cut-off

Figure 3.14: Line with multiple segments in case (i).

Proof. Let’s take Figure 3.14 as an example where the first-period cut-off divides a “hide”

segment. Assume towards a contradiction that there exists poaching behavior in the left

segment. This means that consumers to the left of θ′buy from firm B at pB

2and to the right

of θ′buy from firm A at pA

2. The consumer located at θ′is indifferent between providing

and hiding data. The cost of each option should be the same for this indifferent consumer,

i.e., pB

2+ (¯

θ−θ′) = pA

2+θ′. However, consumers located to the left of θ′who buy from

firm B at pB

2, have an incentive to deviate. By deviating to hide data, the total cost of

buying from firm A would be strictly smaller than the cost before.54 The same method

can be applied to the case when the first-period cut-off divides the “give” segment, which

together shows that if there is poaching behavior in the lateral segments, consumers have

an incentive to deviate, such that a separating equilibrium in pure strategies cannot exist.

From Lemma 8 we can generally infer that in a separating equilibrium firms give up their

option to price discriminate since the cut-offs between lateral segments the following must

hold: pi

2=pi

2,i,∀i=A, B. Based on Lemma 8, we show the non-existence of a separating

equilibrium in pure strategies under exclusive data.

54Assume that they are located at θ′′ with θ′′ < θ′. Since they buy from Firm B at pB

2, the

initial costs are pB

2+(¯

θ−θ′′), which is strictly larger than pB

2+(¯

θ−θ′). By deviating to hide their

data, the total costs would be pA

2+θ′′, which is strictly smaller than pA

2+θ′. Combining together

we can get that pA

2+θ′′ < pA

2+θ′=pB

2+ (¯

θ−θ′)< pB

2+ (¯

θ−θ′′), which shows the benefit from

deviation.

3.5. APPENDIX – THEORETICAL PART

Similar to the previous proof of Proposition 2, we distinguish between two cases: (i)

when the first-period cut-off divides a “hide” segment, and (ii) when the first-period cut-off

divides a “give” segment. Combining with the number of the segments along the line, we

need to, again, check four possible scenarios separately.

Let’s first consider case (i) with multiple segments. As mentioned in Figure 3.14, we

assume towards a contradiction that there is a separating equilibrium with pure strategies.

In order for such a separating equilibrium to exist Lemma 8 must hold and poaching

behavior in lateral segments is excluded, which means that firms cannot poach with their

new customer prices in “give” segments. Again, this implies that firms give up the option

to price discriminate in pure-strategy separating equilibria, which is directly shown from

2=pi

2,i. Yet, it is obvious that firms have an incentive to price discriminate on consumers

who share their data. By increasing their loyalty prices when consumers are segmented as

in the figure above, firms gain by giving up less rent to the consumers. This is a direct

contradiction to the existence of a possible separating equilibrium.

0¯

give hide

first-period cut-off

Figure 3.15: Line with two segments in case (i).

Then we look at the scenario with just two segments in case (i). If there exists such a

separating equilibrium as in Figure 3.15, from Lemma 8 we find no poaching behavior

in the “give” segment. Moreover, based on the customer indifferent between hiding and

sharing data, we have pA

2,A =pA

2. Please note that under such circumstances the firms

again give up price discrimination. However, firm A has an incentive to raise the loyalty

price pA

2,A. By doing so they get more profit from loyal customers and not affect the profit

from anonymous customers. Therefore, this structure is not possible and we can conclude

that there is no separating equilibrium in pure strategies in case (i).

0¯

hide give hide

first-period cut-off

Figure 3.16: Line with multiple segments in case (ii).

In case (ii) when the first-period cut-off divides a “give” segment, let’s first look at the

scenario with multiple segments along the line. In Figure 3.16, by Lemma 8 we know that

there is no poaching behavior in the lateral segments. This means that pA

2,A =pA

2and

3.5. APPENDIX – THEORETICAL PART

2,B =pB

2, and firms give up their option to price discriminate in the lateral segments.

Now, we focus on the central “give” segment. To the left of the first-period cut-off, all

consumers face pA

2,A from firm A and pB

2from firm B. Similarly, to the right of this cut-off,

all consumers choose between pA

2from firm A and pB

2,B from firm B. Given the fact that

2,A =pA

2and pB

2,B =pB

2, the second-period cut-offs in these two intervals coincide, which

means that θA

2=θB

2. Considering the location of θA

2and θB

2, there are three possibilities:

to the left of the first-period cut-off, to the right of the first-period cut-off, and coinciding

with the first-period cut-off.55 If θA

2and θB

2are to the left of the first-period cut-off, no

consumers located to the right of the first-period cut-off buy from firm A at pA

2. However,

in such a condition, firm A has an incentive to raise pA

2in order to get more profit. Thus,

we can rule out this possibility. Similarly, if θA

2and θB

2are to the right of the first-period

cut-off, no consumers located to the left of the first-period cut-off will buy from firm B at

2and firm B would like to increase their new customer price. Therefore, this possibility

is also excluded. Finally, if θA

2and θB

2coincide with the first-period cut-off, no customers

in the central “give” segment buy from firm A at pA

2or from firm B at pB

2. Under such

circumstances, both firm A and firm B have an incentive to raise their new customer

prices and they benefit from this deviation. Overall, we have shown that no separating

equilibrium exists in this scenario.

θ′

0¯

hide give

first-period cut-off

Figure 3.17: Line with two segments in case (ii).

Finally, we check the scenario with just two segments when the first-period cut-off divides

the “give” segment. Firstly, in the “give” segment, there should be some consumers buying

from firm A at pA

2,A and some buying from firm B at pB

2,B. Otherwise, since pA

2,A and pB

2,B

are exclusively set in this segment, either pA

2,A or pB

2,B should be zero and some outside

consumers will deviate to this interval. Then, similar to Lemma 8, we can easily show

that there is no poaching behavior in the “hide” segment and pA

2=pA

2,A. Under such

circumstances, there are two groups of consumers buying from firm A at pA

2on this line:

those who choose to hide their data and those who share their data and buy from firm

B in the first stage. Apparently, due to the higher transportation cost, the second group

of consumers has an incentive to deviate. They would choose to hide their data in the

first stage, and the structure of this separating equilibrium collapses accordingly. As a

summary, we can conclude that no separating equilibrium in pure strategies exists in case

(ii). This completes the proof.

55Please note that θA

2and θB

2do not need to be within the central “give” segment. All results

hold even if they are not within the central “give” segment.

3.6. APPENDIX – EXPERIMENTAL PART

3.6 Appendix – Experimental Part

Instructions for the Market Game

[Text in brackets was not observed by the subjects.]

Welcome to the experiment! From now on, please do not talk to the other participants in

the experiment.

The experiment consists of three parts. In the experiment you will make simple deci-

sions on the computer. All decisions remain anonymous. This means that you do not

learn the identity of the other participants and no participant learns your identity. Your

payout depends on your decisions and the decisions of the other participants. All monetary

information within the experiment is given in ECU (Experimental Currency Unit). Please

read the instructions carefully. If you don’t understand something, please show it with a

hand signal. We will then come to you and answer your questions privately. Below are the

instructions for the first part of the experiment. These are identical for all participants in

the experiment.

A market

Participants in the experiment assume the role of buyers or sellers and are active in mar-

kets with eight locations for two periods. Two sellers sell the same good and are located

on either end of the market. Six buyers are located between the two sellers according to

the following graphical depiction:

Seller

Location 1

Buyer

Location 2

Buyer

Location 3

Buyer

Location 4

Buyer

Location 5

Buyer

Location 6

Buyer

Location 7

Seller

Location 8

Buyers buy exactly one good in each of the two periods. Sellers choose prices pat the

beginning of each period. Prices must be integers between 0and 10. Buyers pay the price

of a good and transportation costs taccording to their distance to the respective seller.

Buyers pay transportation costs of one unit per field and have to move to the sellers’

location (Example: A buyer at location 5 pays a transportation cost of 4 to the seller at

location 1 and of 3 to the seller at location 8). Buyers receive earnings according to the

following earnings function:

Earnings = 15 −p−t

At the beginning of the first period sellers choose an introduction price for the first period.

Buyers choose one seller and decide whether to allow tracking of their purchase activity.

At the beginning of the second period sellers choose three prices: [Open data treatment]

anew customer price for buyers, who do not allow tracking of their purchase activity; a

loyalty price for their customers of the first period, who allow tracking of their purchase

3.6. APPENDIX – EXPERIMENTAL PART

activity and a poaching price for customers of the other seller, who allow tracking of their

purchase activity. [Exclusive data treatment] a loyalty price for their customers of the

first period, who allow tracking of their purchase activity and a new customer price for

customers of the other seller, who allow tracking of their purchase activity, as well es for

buyers, who do not allow tracking of their purchase activity. [End treatments] The profit

in ECU of a seller in a round corresponds to the sold number of goods nmultiplied with

their respective price paccording to the following profit function:

Profit =p·n

Price table

[Open data treatment]

Chosen seller

in first period

Allow tracking

of purchase activity

Price of

seller 1

Price of

seller 2

Seller 1 allow Loyalty price New customer price

Seller 1 don’t allow New customer price New customer price

Seller 2 allow New customer price Loyalty price

Seller 2 don’t allow New customer price New customer price

[Exclusive data treatment]

Chosen seller

in first period

Allow tracking

of purchase activity

Price of

seller 1

Price of

seller 2

Seller 1 allow Loyalty price Poaching price

Seller 1 don’t allow New customer price New customer price

Seller 2 allow Poaching price Loyalty price

Seller 2 don’t allow New customer price New customer price

[End treatments]

Observed prices of buyers in the second period depending on their first period purchasing

and tracking decision.

Summary of a market

First period

•Sellers set the introductory price for the first period

•Buyers make their first purchase decision

•Buyers allow or disallow tracking of their purchase activity

Second period

[Open data treatment]

3.6. APPENDIX – EXPERIMENTAL PART

•Sellers set the new customer price, poaching price and loyalty price for the second

period

[Exclusive data treatment]

•Sellers set the new customer price and loyalty price for the second period

[End treatments]

•Buyers perceive prices according to their purchase decision and their decision to

track purchase activity in period 1

•Buyers make their first purchase decision

Duration and procedure of the experiment

At the beginning of the experiment each participant is assigned a role, which remains fixed

for the remainder of the experiment of 20 rounds in total. In each round there are two

markets with two sellers each. Six buyers are active in both markets, while sellers are

active in one of the markets. Within one round locations of buyers and sellers are fixed.

Each round buyers are assigned random new locations in both markets. Sellers are ran-

domly assigned to one market with a random location at either end of the market in each

round.

Payout in the experiment

Your profit, respectively your earnings, for the entire experiment are your cumulative prof-

its, respectively earnings, across all rounds. At the end of the experiment your profits,

respectively earnings, are converted into euros at the rate 10 ECU = 0.20 Euro. This

amount will be paid to you privately and in cash after the experiment, together with an

entry fee of 5 Euro and your payouts of part two and part three.

Once you have finished reading the instructions you can start answering the review ques-

tions on the last page.

Review Questions

Before the experiment starts, it should be ensured that all participants have understood

the instructions of the experiment. Please mark the correct statements for each question.

Your answers will not affect your payout and you can always ask questions. To do this,

please raise your hand and wait for someone to come to you to answer your question. Once

you have finished answering the questions, please raise your hand. An experimenter will

come to you and check your answers.

Question 1. Which of the following statements about the sellers is true?

a) Throughout one round, the two sellers within a market are the same two participants

in the experiment.

3.6. APPENDIX – EXPERIMENTAL PART

b) Throughout every round, the two sellers within a market are the same two participants

in the experiment.

Question 2. What price does a buyer observe from a seller in the second period if they

bought from the same seller in the first period and allow tracking of purchase activity?

[Open data treatment]

a) Loyalty price b) Poaching price c) New customer price

[Exclusive data treatment]

a) Loyalty price b) New customer price

[End treatments]

Question 3. What price does a buyer observe from a seller in the second period if

they bought from the opposite seller in the first period and allow tracking of purchase

activity?

[Open data treatment]

a) Loyalty price b) Poaching price c) New customer price

[Exclusive data treatment]

a) Loyalty price b) New customer price

[End treatments]

Question 4. What price does a buyer observe from a seller in the second period if they

bought from the same seller in the first period and do not allow tracking of purchase

activity?

[Open data treatment]

a) Loyalty price b) Poaching price c) New customer price

[Exclusive data treatment]

a) Loyalty price b) New customer price

[End treatments]

Question 5. What price does a buyer observe from a seller in the second period if

they bought from the opposite seller in the first period and do not allow tracking of

purchase activity?

[Open data treatment]

a) Loyalty price b) Poaching price c) New customer price

[Exclusive data treatment]

a) Loyalty price b) New customer price

[End treatments]

3.6. APPENDIX – EXPERIMENTAL PART

The Game of 22

The iterative thinking task is a variation of the “Game of 21” (Dufwenberg et al., 2010;

Gneezy et al., 2010). In our version, players take turns increasing a counter that starts at

0by increments of 1,2or 3. The game ends when either of two players reaches 22, where

the player who picks 22 loses. Thereby, the game stays true to the original variation, where

the player who picks 21 wins the game directly. The winning path constitutes of picking

any number that is a multiple of three. Instead of using an interactive game between

two subjects as intended in the original variation, we let each subject play against the

computer. This is necessary in order to gather a measure on correct iterative reasoning for

every subject.56 Subjects learn that they play against the computer, without any detailed

explanation on how the computer chooses. Unknown to the players, the computer avoids

winning, while randomizing between the two or three available options57. This is necessary

so that we can capture the exact turn in which participants realized how to win the game.

Instructions for the Game of 2258

The rules of the game are as follows: This is a two-player game in which players increase

a counter. This counter starts at 0 and ends at 22 and must be moved each turn by 1, 2

or 3 steps, with players acting sequentially. You will play this game against the computer

and you are the first to move. The player who reaches 22 loses. If the computer loses the

game, you will earn EUR 2, while you will earn EUR 0 if you lose.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

Figure 3.18: Representation of the Game of 22.

56If two players interact and one plays the optimal strategy, no conclusions can be drawn

concerning the other player.

57Whenever the player is on the winning path, the computer randomizes between all three

options, while only randomizing between the two options which avoid the winning path, whenever

the player is not on the winning path.

58Instructions are originally in German and presented on screen.

3.6. APPENDIX – EXPERIMENTAL PART

Results of the Game of 22

Figure 3.21 shows the distribution of scores in the Game of 22. The score represents the

number of consecutive turns on the winning path before the game ended. Our findings

are in line with Dufwenberg et al. (2010) where the majority of subjects are able to solve

two steps of backward induction (mean: 2.01, median: 2, mode: 2 ). In contrast to their

results our subjects did not show an ability to immediately solve the game, with barely

anyone solving the full six steps of induction. Overall, the results suggest that the game

is suitable as a rough measure of iterative thinking capability and we cannot detect any

differences between our treatments, χ2(6, N = 80) = 0.8359, p = 0.991.

Privacy Concern Survey (IUIPC Score)59

All statements are rated by the subjects on a seven-point scale from “strongly agree” to

“strongly disagree”. The first three statements relate to control issues, statements four to

six relate to awareness and the remaining four statemtents relate to collection issues.

1) Consumer online privacy is really a matter of consumers’ right to exercise control

and autonomy over decisions about how their information is collected, used, and

shared.

2) Consumer control of personal information lies at the heart of consumer privacy.

3) I believe that online privacy is invaded when control is lost or unwillingly reduced

as a result of a marketing transaction.

4) Companies seeking information online should disclose the way the data are collected,

processed, and used.

5) A good consumer online privacy policy should have a clear and conspicuous disclo-

sure.

6) It is very important to me that I am aware and knowledgeable about how my personal

information will be used.

7) It usually bothers me when online companies ask me for personal information.

8) When online companies ask me for personal information, I sometimes think twice

before providing it.

9) It bothers me to give personal information to so many online companies.

10) I’m concerned that online companies are collecting too much personal information

about me.

59Original questions of Malhotra et al. (2004) were translated to German.

3.6. APPENDIX – EXPERIMENTAL PART

The Role of Privacy Concern

In this section, we take a deeper look into our control measure of privacy concern and

how it relates to information disclosure. Our observed IUIPC-scores are depicted in Figure

3.22. The distributions do not show treatment differences, t(158) = 1.4147, p = 0.1591.

However, there is a general tendency towards high privacy concern among our subjects.

Going forward, we classify our subjects into three groups, using the median (0.2014) as an

initial breaking point and 1-median (1−0.2014 = 0.7986) as the second breaking point. We

classify a score below the median as “privacy concerned”, a score between the median and

1-median as “privacy considerate”, and a score above 1-median as “privacy unconcerned”.

By nature of this classification, half of our subjects fall into the first category of concerned,

while surprisingly not a single subject falls into the last category of unconcerned. Thus,

the remaining half of the subjects are “considerates”.60

0 5 10 15 20

Round

Concerned Considerate

(a) Open data treatment

0 5 10 15 20

Round

Concerned Considerate

(b) Exclusive data treatment

Figure 3.19: Share of tracking allowed over periods by Treatment and privacy concern.

In Figure 3.19, we show the average rate of information disclosure over period by treatment

and privacy concern classification. There are two major observations here. In the open

data treatment “concerned” and “considerate” buyers have a similar sharing rate. In the

exclusive data treatment “considerate” subjects have a lower sharing rate than “concerned”

subjects, which relates to the privacy paradox.61 Moreover, we find that the initially large

sharing rate in the exclusive data treatment is largely driven by “concerned” subjects.

Beresford et al. (2012); Preibusch et al. (2013) find that subjects did not act according

to their stated privacy preferences when faced with a market environment. This is also

reflected in Figure 3.19 where more concerned participants are actually sharing more in-

formation. However, for both privacy concerned and considerate buyers we see a drop in

60Among the considerates we also observe a tendency leaning towards privacy concern. More-

over, irrespective of the final score, all subjects expressed concern at least once within the 10 item

questionnaire.

61Acquisti et al. (2016) and Dinev and Hart (2006) explain the paradox with a privacy calculus

model, which describes a mental negotiation of benefits versus concerns from disclosing information

in an e-commerce setting.

3.6. APPENDIX – EXPERIMENTAL PART

information sharing over periods, where particularly considerate buyers in the exclusive

data treatment drop below the sharing rates of the remaining three groups in the last 10

rounds.

close mid far

Proximity to closest seller

Concerned Considerate

(a) Open data treatment

close mid far

Proximity to closest seller

Concerned Considerate

(b) Exclusive data treatment

Figure 3.20: Share of tracking allowed per location by Treatment and privacy concern.

Next, we investigate whether similar discrepancies are present in the locational informa-

tion disclosure between privacy types. In Figure 3.20, we show how information disclosure

depends on consumers’ locations under classification between privacy types. This ties in

directly with our theoretical analysis which largely relies on the pooling assumption in

the construction of equilibria. Again, we differentiate between “concerned” and “consider-

ate” consumers. Figure 3.20 depicts that there is no locational preference for information

disclosure in case of “concerned” consumers for both treatments. However, “considerate”

consumers share less information than “concerned” consumers in the exclusive data treat-

ment. This is true for all locations and is considerably balanced.

The time trend did not reveal an impact of privacy concern on information disclosure

in the open data treatment, but we find an impact of location in the case of considerate

consumers. Considerate subjects in the open data treatment are less likely to share infor-

mation at the “far” locations than concerned subjects, χ2(2, N = 670) = 7.50, p < 0.03.

In comparison to concerned consumers we find that considerate consumers share slightly

more information in close and mid locations and less information in the far location.62

These counteracting effects cancel each other out, so that the average disclosure rate of

considerate consumers is similar to the disclosure rate of concerned consumers. While we

cannot explain this behavior on theoretical grounds, we can suggest that considerate con-

sumers are more involved when it comes to disclosure of private information and both the

data policy (open and exclusive data) and the individual preferences (where preferences

are described by location) are factored into the decision. Overall, this extends our evidence

62These deviations relate to Lemma 3 and 7 in that the most probable deviations are suspected

in the central locations. The according response by sellers is setting the loyalty price equal to the

new customer price. This corresponds to the pricing observations we have shown earlier.

3.6. APPENDIX – EXPERIMENTAL PART

towards Hypothesis 3. That is, in the second half we observe less information sharing in

the exclusive data treatment, which is mainly driven by privacy “considerate”, i.e. less

concerned subjects. This is akin to the commonly observed privacy paradox. Those who

express more concern about privacy issues are not consistently acting on it.

In Table 3.13, we include a Considerate dummy, as well as an interaction of Considerate

with the treatment and second-half dummies. The main effects that we have shown in

Table 3.8 still hold when allowing for this richer interaction with privacy concern. Moreover,

we can confirm the results we discussed before. Concerned (considerate) subjects share

more (less) information in the exclusive treatment, while the sharing rate is decreased in

the last ten rounds.

Additional Figures and Tables

Frequency

0 2 4 6

Game of 22 score

Open data

Exclusive data

Figure 3.21: Game of 22 scores by Treatment.

concerned

considerate

unconcerned

Frequency

0 .2 .4 .6 .8 1

IUIPC score with median (dashed)

Open data

Exclusive data

Figure 3.22: IUIPC scores by Treatment.

3.6. APPENDIX – EXPERIMENTAL PART

0 5 10 15 20

Round

Predicted first-period price Observed first-period price

Predicted new customer price Observed new customer price

Predicted loyalty price Observed loyalty price

Predicted poaching price Observed poaching price

Figure 3.23: Observed and predicted prices in the open data treatment.

0 5 10 15 20

Round

Predicted first-period price Observed first-period price

Predicted loyalty price Observed loyalty price

Predicted new customer price Observed new customer price

Figure 3.24: Observed and predicted prices in the exclusive data treatment.

3.6. APPENDIX – EXPERIMENTAL PART

Location

2 3 4 5 6 7 Total

Open data treatment

Purchasing order (b1, b2)

(A, A) 92.50% 83.12% 43.12% 5.62% 1.88% 0.31% 37.76%

(A, B) 3.12% 9.06% 25.94% 20.94% 7.50% 0.94% 11.25%

(B, A) 2.81% 5.62% 23.12% 29.38% 1.88% 0.31% 11.93%

(B, B) 1.56% 2.19% 7.81% 44.06% 83.44% 95.31% 39.06%

Information disclosure 67.50% 69.38% 62.81% 61.88% 70.00% 71.56% 67.19%

Exclusive data treatment

Purchasing order (b1, b2)

(A, A) 96.25% 89.38% 57.50% 10.31% 0.94% 0.62% 42.50%

(A, B) 2.19% 3.75% 18.75% 18.12% 7.19% 2.50% 8.75%

(B, A) 1.56% 5.31% 14.69% 15.31% 3.44% 1.56% 6.98%

(B, B) 0.00% 1.56% 9.06% 56.25% 88.44% 95.31% 41.77%

Information disclosure 60.94% 62.19% 69.38% 67.19% 65.31% 67.19% 65.36%

Seller Ais located at location 1, seller Bis located at location 8, just outside the depicted

locations. (b1, b2)is the purchase order, where b1∈ {A, B}is the first period purchase and

b2∈ {A, B}is the second period purchase.

Table 3.11: Share of purchasing orders and information disclosure by treatment and location.

Bought from far seller in period 1

at same total costs ∈ {0,1}

(1) (2) (3) (4)

Exclusive -1.168∗∗∗ -1.194∗∗∗ -1.191∗∗∗ -1.198∗∗∗

(0.332) (0.304) (0.336) (0.297)

Allow tracking 0.404 0.489

(0.361) (0.383)

Second half 0.226 0.177

(0.298) (0.331)

Market No Yes No Yes

Location No Yes No Yes

Demographics No Yes No Yes

Privacy concern No Yes No Yes

Iterative thinking No Yes No Yes

Observations 310 297 310 297

Standard errors in parentheses. Estimation by random-effects logistic regression with clustering

on group level. ∗,∗∗ and ∗∗∗ denote significance at the 10%, 5% and 1% level, respectively.

Table 3.12: Impact of treatment, tracking and learning on purchasing decision when total costs

are equal.

3.6. APPENDIX – EXPERIMENTAL PART

Tracking allowed ∈ {0,1}

(1) (2) (3) (4)

Exclusive 0.543∗∗ 0.655 0.891∗∗∗ 1.004∗∗

(0.253) (0.436) (0.310) (0.471)

Considerate 0.029 0.106 -0.065 0.008

(0.335) (0.366) (0.387) (0.410)

Exclusive ×Considerate -1.008∗∗ -1.705∗∗∗ -0.900 -1.601∗∗∗

(0.499) (0.468) (0.587) (0.549)

Second half -0.142 -0.144

(0.201) (0.199)

Exclusive ×Second half -0.626∗-0.619∗

(0.339) (0.336)

Considerate ×Second half 0.187 0.194

(0.226) (0.219)

Exclusive ×Considerate ×Second half -0.265 -0.291

(0.406) (0.402)

Market No Yes No Yes

Location No Yes No Yes

Demographics No Yes No Yes

Iterative thinking No Yes No Yes

Observations 3840 3800 3840 3800

Standard errors in parentheses. Estimation by random-effects logistic regression with clustering

on group level. ∗,∗∗ and ∗∗∗ denote significance at the 10%, 5% and 1% level, respectively.

Table 3.13: Interaction between privacy concern and learning.

Chapter 4

Rebate Rules in Reward-based Crowdfunding:

Introducing the Bid-cap Rule63

4.1 Introduction

Crowdfunding is the practice of raising capital from many people through an on-

line platform and is quickly expanding worldwide (Agrawal et al., 2014). There

exist several reasons for project creators and contributors, commonly referred to

as (project) backers, to use crowdfunding. Project creators that have traditionally

relied on other sources like banks or venture capitalists can raise funds directly from

a large base of backers to realize projects. Crowdfunding also provides project cre-

ators that have limited access to traditional financing sources with a new channel to

raise money and pursue their projects. Furthermore, crowdfunding can increase the

popularity of a project and can stimulate long-term customer acquisition (Gerber

and Hui, 2013). On the demand side, backers can be part of a community, support

similarly interested people, or get compensation (Deb et al., 2019).

In this paper, we focus on reward-based crowdfunding, where backers receive

direct non-monetary rewards for their pledge to a project if their pledge exceeds a

pre-set entry fee.64 By virtue of this funding scheme, project backers are not only

customers but also the investors of the project creator, i.e., reward-based crowdfund-

63This chapter is the accepted manuscript published as: Gerstmeier, F., Oezcelik, Y., and

Tolksdorf, M. (2023). Rebate Rules in Reward-Based Crowdfunding: Introducing the Bid-Cap

Rule. Collaborative Research Center Transregio 190, Discussion Paper No. 392.

64Such rewards can take on various forms such as early access to a product, a limited version of

a product or some forms of individualization, like signed or otherwise customized products. The

pre-set entry fee corresponds to minimum amounts that have to be pledged to receive the goods

or perks.

4.1. INTRODUCTION

ing allows project creators to contract the purchasing decision before investments

into productions are made and thus sunk. The rapid expansion of crowdfunding in

many countries has given rise to multiple large-scale crowdfunding platforms such

as Kickstarter, GoFundMe, and Indiegogo. As a result, the global reward-based

crowdfunding market achieved a $13.64 billion market value in 2021, forecast to

double by 2028 with an annual expected growth rate of 11% (Statista, 2021).

Crowdfunding platforms match supply, funding, and demand via a mechanism

where the all-or-nothing and keep-it-all models are most commonly used. Under the

all-or-nothing model, project creators get all pledges if the funding goal is reached,

while all pledges are paid back otherwise. In contrast, under the keep-it-all model,

the project creators receive all pledges accumulated during the funding time, inde-

pendent of whether the funding goal is reached. Comparing these two models, it

is commonly understood that the all-or-nothing model is superior to the keep-it-all

model by attracting higher pledges and yielding more project successes (see Coats

et al., 2009; Cumming et al., 2020; Wash and Solomon, 2014). The all-or-nothing

model is particularly popular in reward-based crowdfunding, as it is a screening

device that helps to reduce demand uncertainty (Strausz, 2017; Chemla and Tinn,

2020; Xu and Ni, 2022).

Similar to conventional financial markets, not all demand for funding can be

satisfied on crowdfunding platforms. Around 60% of projects on Kickstarter failed

to reach the self-set funding goal as of March 2023.65 While many failed projects are

far from reaching the funding goal, some projects are just shy of the funding goal

when the funding period ends. For these projects, a small increase in pledges could

mean project success. This issue is particularly critical under the all-or-nothing

model, common in reward-based crowdfunding, where project creators only obtain

the pledges when the funding goal is reached. Hence, project creators (and crowd-

funding platforms) want to find ways to either reach new backers or increase the

pledges of existing backers if the opportunities for attracting additional backers are

exhausted.

Several studies focus on ways to increase the number of backers and improve

the coordination between backers, e.g., by encouraging early pledges (Ansink et al.,

2017; Solomon et al., 2015), disseminating positive opinions (Comeig et al., 2020),

highlighting specific projects (Corazzini et al., 2015), giving greater project involve-

ment to customers (Cornelius and Gokpinar, 2020; Regner and Crosetto, 2021), and

the timing of promotions (Regner and Crosetto, 2018; Li and Wang, 2019). How-

ever, exploring ways to induce a given number of backers to increase their pledges

65See https://www.kickstarter.com/help/stats?ref=global-footer for more information.

4.1. INTRODUCTION

has received little attention in the crowdfunding literature. In this case, raising

funds to reach the funding goal can be viewed as a residual threshold public good

game among all investing backers. One solution to overcome the residual public

good problem is refund bonuses. Refund bonuses are granted to backers in addition

to their pledge when the funding goal is not met, i.e., when projects are unsuccess-

ful. Cason and Zubrickas (2017, 2019) find that contributors respond to incentives

induced by refund bonuses in line with predictions and that refund bonuses can

increase project realization rates substantially. Cason et al. (2021) scrutinize the

dynamics of funding by focusing on refund bonuses that are only rewarded to early

contributors in case of fundraising failure. They find that offering refund bonuses

only to early contributors works just as well as offering a refund bonus to every con-

tributor. However, as refund bonuses are granted upon project failure, it remains to

be clarified who would pay for them since neither project creators nor crowdfunding

platforms may have the necessary funds.

The threshold public goods literature identifies rebating excess contributions

back to contributors when the total contributions exceed the provision point as

another way to increase contributions and project success rates. Smith (1980) origi-

nally proposed a proportional rebate rule in public good auctions. Marks and Croson

(1998) and Rondeau et al. (1999) introduced this rebate rule in provision point mech-

anisms by rebating excess contributions proportionally back to contributors when

the provision point is exceeded. Marks and Croson (1998) compare contributions in

the presence and absence of proportional rebates and a utilization rule. They find

that under rebate rules, similar contributions are obtained as without rebates, and

contributions were highest when excess contributions were utilized via a secondary

standard public good. Rondeau et al. (1999) show that a provision point mecha-

nism with proportional rebates can be empirically demand-revealing. Besides the

proportional rebate rule, Spencer et al. (2009) consider five alternative rebate rules,

including variations of lottery-like winner-take-all rules and random rebate rules.

They find that for all rules, total contributions equal total benefits or exceed them.

Our main contribution to the crowdfunding literature is the development of a

new rebate scheme which we call the bid-cap rule. The bid-cap rule sets an ex-

post limit on pledges such that the funding goal is exactly reached. Pledges above

this limit are reduced to the cap making it less risky to pledge greater amounts.

We additionally adapt the proportional rebate rule to a reward-based crowdfunding

framework. Under this rule, backers are not rebated proportionally to their pledge

but proportionally to the part of their pledge that exceeds the pre-set entry fee. We

then experimentally test both rebate rules against the all-or-nothing model and each

4.2. THE GAME

other regarding backer’s pledges and project success rates. By design of the rebate

rules, all backers receive a rebate under the proportional rebate rule, while under the

bid-cap rule, only those who pledge the most, i.e., those who pledge more than the

cap, receive a rebate. Theoretically, the bid-cap rule induces weakly less variance in

payments upon project realization and rewards those who pledge the most compared

with the proportional rebate rule. However, how this affects pledging behavior is

ambiguous as it could also induce higher pledges due to decreased perceived risk

and reinforce free-riding behavior. With our experiment, we show that both rebate

rules substantially increase backer pledges and the project realization rate compared

with the all-or-nothing model, while we can confirm that the variance of payments

is lower under the bid-cap rule compared with the proportional rebate rule.

4.2 The Game

Consider a static game with Nindividuals, respectively backers, where each backer

i∈ {1, . . . , N}has an endowment of Ei. Each backer can decide on a pledge

bi∈[0, Ei]that is used for the realization of a project. The project is realized if

the total pledges ∑biweakly exceed an exogenously given provision point PP.66 If

the total pledges are short of PP each backer gets back their pledge biand pays 0.

To capture the nature of reward-based crowdfunding, a backer receives their private

valuation vifrom the realized project if and only if they pledge more than a pre-set

reservation price of r. Hence, if the project is realized but backer ihas pledged

bi< r, they will not receive their valuation from the project, while all backers

with bi≥rwill receive their valuation vifrom the project. Pledges below rare

collected and are considered donations toward the realization of the project.67 In

the following, n≤Nis the number of backers pledging at least r, and N−nis the

number of backers with pledges bi∈[0, r).

We assume that ∑vi> PP such that the realization of the project is socially

desirable as its total benefits exceed the costs of provision. Further, we will focus on

the cases where PP > N ·r, i.e., pledging has a public good character in addition to

the inherent purchasing decision, as these are the cases in which the all-or-nothing

model is prone to fail.

When the total pledges exceed the provision point, the excess pledges may be

reallocated back to the backers who pledged at least ror may be kept in the project

66Throughout ∑always represents ∑N

i=1 if not stated otherwise.

67Reservation prices are commonly observed on crowdfunding platforms such as Kickstarter,

Indiegogo, and StartNext, where project creators post a minimal price which backers have to

pledge to receive the good but are allowed to pledge more or less than the reservation price.

4.2. THE GAME

yielding no additional benefit to backers. The latter corresponds to the all-or-nothing

model. We further consider the case where the excess pledges are rebated to backers

proportional to the amount their pledges exceed the reservation price. Additionally,

we develop the new bid-cap rebate rule, where an ex-post limit on payments is

determined such that either the provision point is met exactly or backers pay the

reservation price at most. Details for these rebate rules and the individual payoff

function according to these rules are explained below.

All-or-nothing model

Under the all-or-nothing model, excess pledges above PP are not rebated to backers.

The individual payoff πiis given by

πi=⎧

⎪

⎨

⎪

⎩

Ei−bi+viif ∑bi≥PP and bi≥r

Ei−biif ∑bi≥PP and bi< r

Eiif ∑bi< PP

.(4.1)

The marginal penalty associated with over-pledging is

∂πi

∂bi

=−1,(4.2)

meaning that while the provision point is met, an increase of backer i’s pledge by

one reduces backer i’s payoff by the same amount.68

Proportional rebate rule

In our adaption of the proportional rebate rule to the reward-based crowdfunding

case, excess pledges are rebated proportional to the difference between pledge and

reservation price ei:= max{0, bi−r}to those backers who pledged at least r.69 The

reservation price is often set at marginal cost, whereby a company would make a

loss if backers paid less than r. The individual payoff πiis

πi=⎧

⎪

⎨

⎪

⎩

Ei−bi+vi+ei

∑ei(∑bi−PP)if ∑bi≥PP and bi≥r

Ei−biif ∑bi≥PP and bi< r

Eiif ∑bi< PP

.(4.3)

68Following the literature we define over-pledging similar to over-contribution as a marginal

increase of biwhile ∑bi≥PP.

69This is in contrast to Rondeau et al. (1999) and Marks and Croson (1998) who rebate pro-

portional to the full contribution in a standard threshold public good game.

100

4.2. THE GAME

The marginal penalty associated with over-pledging is

∂πi

∂bi

=⎧

⎪

⎨

⎪

⎩

−1 + (∑bi−P P )(∑ei−ei)+(ei∑ei)

(∑ei)2if bi≥r

−1if bi< r

.(4.4)

Note that the absolute value of the marginal penalty of over-pledging under the

proportional rebate rule is weakly smaller than under the all-or-nothing model. This

is the case since, given that the project is realized, ∑bi−PP ≥0,∑ei−ei≥0,

and ei∑ei>0so that the second term in the first case must be positive or zero. In

Appendix 4.6.1, we further show that the second term in the first case is smaller than

one such that the penalty of marginally increasing the pledge is strictly negative.

Bid-cap rule

For the bid-cap rule, consider any sequence of pledges by all backers (b1, . . . , bN).

Without loss of generality, we assume b1≤b2≤. . . ≤bN. When total pledges exceed

the provision point, we find a bid-cap ¯

b>rsuch that ∑k

i=1 bi+ (N−k)¯

b=PP,

where ¯

b∈[bk, bk+1)is the cap, i.e., the highest payment any backer has to make.

The bid-cap ¯

bis determined via a recursive algorithm that gradually increases ¯

while backers either pay the bid-cap ¯

bif bi≥¯

bor their individual pledge biif bi<¯

The algorithm stops increasing ¯

bwhen the sum of (capped) pledges is equal to the

provision point PP.70 Hence, kbackers pay their full pledge and N−kbackers pay

the bid-cap ¯

b.71 The individual payoff πiis given as

πi=

⎧

⎪

⎨

⎪

⎩

Ei−bi+vi+ (bi−¯

b)if ∑bi≥PP and bi≥¯

Ei−bi+viif ∑bi≥PP and bi∈[r,¯

Ei−biif ∑bi≥PP and bi< r

Eiif ∑bi< PP

.(4.5)

The marginal penalty associated with over-pledging is

∂πi

∂bi

=⎧

⎨

⎩

0if bi≥¯

−1if bi<¯

.(4.6)

70An explicit example of the procedure is given in the translated instructions, see Page 129 in

the Appendix.

71Note, that the condition ¯

b>rmust be necessarily fulfilled since we only consider cases where

PP > N ·r. For the special case of k= 0 we have r≤¯

b<b1≤. . . ≤bNwhere everything that

follows holds as well.

101

4.2. THE GAME

In Appendix 4.6.2, we show that under the bid-cap rule a solution (k,¯

b)must always

exist. In Appendix 4.6.3, we further show that (k,¯

b)is uniquely determined for any

sequence of pledges.

Note that, similar to the proportional rebate rule, the absolute value of the

marginal penalty of over-pledging under the bid-cap rule is weakly smaller than

under the all-or-nothing model. Further, the absolute value of the marginal penalty

of over-pledging under the bid-cap rule is weakly smaller than under the proportional

rebate rule if bi≥¯

band strictly greater if r≤bi<¯

Comparison of rebate rules

To have a sensible comparison between the rebate rules, we assume the same se-

quence of pledges for both rules and compare the outcomes that different rebate rules

induce. Consider a fixed sequence of ordered pledges (b1, . . . , bN)with ∑bi> PP.

Under the proportional rebate rule, every backer who pledges more than the reser-

vation price rreceives a rebate. In contrast, under the bid-cap rule only backers

i∈ {k+ 1, . . . , N}, i.e., backers who pledged more than ¯

b, receive a rebate. Since

the total amount of rebates cannot change, it follows that backers with high (low)

pledges must be better (worse) off under the bid-cap rule compared with the pro-

portional rebate rule. In fact, we find that the relation of payments is as shown in

Figure 4.1.

Pledge

Payment

0r¯

bˆ

bbN

Proportional rebate

Bid-cap

Figure 4.1: An example of payments by pledge under rebate rules.

All backers below an intersection ˆ

b∈(¯

b, bN)are better off under the proportional

rebate rule, and all backers with pledges above the intersection are better off under

the bid-cap rule. Backers pledging close to (or equal to) ¯

bare worst off under the bid-

cap rule compared with the proportional rebate rule. In Appendix 4.6.4, we show

that these properties hold for any discrete sequence of pledges. A direct consequence

of these findings is that the variance of payments is lower under the bid-cap rule

102

4.3. THE EXPERIMENT

compared with the proportional rebate rule for any given sequence of pledges that,

in sum, exceed the provision point.

4.3 The Experiment

4.3.1 Experimental Design and Procedures

We implemented the game described in Section 4.2 as an experiment with par-

ticipants acting as project creators or backers. Our experiment consisted of three

experimental treatments, following the three cases of our game: all-or-nothing, pro-

portional rebate, and bid-cap. We chose the parameters in the experiment such

that the number of players, aggregate benefits to costs ratio, and share of aggregate

endowment necessary for project realization are in line with past work on threshold

public goods (Croson and Marks, 2000). Each treatment consisted of two parts and

was structured as follows. Participants were randomly assigned to a computer upon

entering the laboratory. Participants then read the instructions for the first part

and could ask questions to ensure comprehension. The instructions for the first part

stated that the participants play the game once. Further, it was mentioned that the

experiment includes a second part but not what the task was in the second part.

The task in the second part, comprising ten repetitions of the same game with ran-

domly determined valuations, was revealed in separate instructions provided after

the first part had elapsed. Since participants did not know that they were playing

the same game in the second part again, we interpret the first round as behavior

in a one-shot game. Comprehension of the instructions of Part 1 was checked with

on-screen control questions, which had to be answered correctly before the first part

started.

Similar to Spencer et al. (2009), we presented our game as an investment game by

referring to pledges as “investments” and the provision point as “investment costs”

in the instructions. The participants were assigned to groups comprising eleven

participants that remained the same throughout the experiment. At the beginning

of the experiment, it was randomly determined whether a participant was active

or passive, with each group consisting of N= 10 active players and one passive

player. The active players represent project backers, while the passive player cor-

responds to a project creator who benefits from the project realization but cannot

actively contribute to the project. In addition, the passive player was paid the ex-

cess pledges in the all-or-nothing treatment if the project was realized. This mimics

actual crowdfunding platforms where excess pledges go to the project owner upon re-

103

4.3. THE EXPERIMENT

alization.72 Moreover, without a passive player, excess pledges would be kept by the

experimenter in the all-or-nothing treatment while they are redistributed among

participants in both rebate treatments, potentially causing experimenter demand

effects. Each participant was endowed with Ei= 65 experimental currency units

(ECU) and each active participant could pledge any amount out of this endowment

toward the realization of a project. The project was only realized if the provision

point of PP = 300 ECU was reached. In contrast to Spencer et al. (2009), we

informed participants about the provision point ex-ante since in crowdfunding the

provision goal is most commonly featured in the project descriptions. If an active

player pledged at least the ex-ante known reservation price of r= 15 ECU, this

participant could obtain a payout upon project realization. Pledges below 15 ECU

did not entitle an active player to the payout. If the total pledges were below the

provision point of 300 ECU, then each participant was refunded their pledge. If the

project was successfully funded, each active player who pledged at least 15 ECU

received their valuation of vi= 45 ECU. This means each active player had the

same project valuation. The passive player received 65 ECU independent of project

realization and received an extra 45 ECU if the project was realized. If the total

pledges exceeded the provision point of 300 ECU, the excess amount was rebated

to the active players in the proportional rebate and bid-cap treatments according

to the respective applied rebate rule, while the passive player received the excess

amount in the all-or-nothing treatment.

After the first part had ended, each participant received additional instructions

for Part 2, i.e., the repeated version of the game. Importantly, participants did not

receive any feedback about the outcome of the first part after it had elapsed. The

second part was almost identical to the first, with two major changes. The game

was repeated for ten rounds, and the value active players ascribed to the project was

heterogeneous. The valuation was a whole number drawn each round from a uniform

distribution with support [30,60]. Thereby, the minimum aggregate project value

for the active players was 300 ECU, which covered the costs of project realization.

The actual realized minimum aggregate project value of the active players was 350

ECU with an average of 442.41 ECU. Participants received no feedback between

the rounds, eliminating any feedback effects. Again, the comprehension of these

instructions was checked via on-screen control questions. The payoff for the second

part equaled the payoff obtained in a randomly drawn round, where each round is

equally likely to be chosen. Each participant’s final payoff was the sum of their first

and second part payoffs.

72All theoretical results from section 4.2 hold with the passive player.

104

4.3. THE EXPERIMENT

The experiment was conducted at Technische Universität Berlin in November

2022. The experiment was programmed with the experiment software z-Tree (Fis-

chbacher, 2007a). In total, 132 Participants were recruited using ORSEE (Greiner,

2015a). We conducted six sessions, two sessions per treatment, with 22 participants

each. The (translated) experimental instructions can be found in the Appendix.

Sessions lasted around 30 minutes. Participants earned 10.89 EUR on average, in-

cluding a show-up fee of 6 EUR.

4.3.2 Hypotheses

The all-or-nothing model and both rebate rules underlying the experimental treat-

ments share the same inefficient and efficient Nash equilibria. In inefficient Nash

equilibria, the project is not realized and no backer can increase their pledge to

achieve realization. Efficient Nash equilibria are any combinations of individually

rational pledges (bi≤vi) that exactly sum up to the provision point.73 Nonetheless,

the proportional rebate rule and the bid-cap rule better the outcome of some (or all)

backers in the off-path cases, where the sum of pledges strictly exceeds the provision

point. Due to this, higher pledges come with lower risk under the rebate rules, as

also indicated by the lower marginal penalty for all pledges above the reservation

price (bi> r) under the proportional rebate rule, as shown in equation (4.4) and for

all pledges above the bid-cap (bi>¯

b) under the bid-cap rule as shown in equation

(4.6). This leads to our first hypothesis.

Hypothesis 1: The pledges will be higher under the rebate rules compared with the

all-or-nothing model.

As a consequence of Hypothesis 1, we expect that the pledges are sufficiently in-

creased under the rebate rules compared with the all-or-nothing model to positively

affect the probability of a project realization, yielding our second hypothesis.

Hypothesis 2: The project realization rates will be higher under the rebate rules

compared with the all-or-nothing model.

Conditional on project realization, the mean payments of active players are PP/N =

30 by design under both rebate rules. Hence, we can only expect differences in the

distributions of payments. Given that the bid-cap rule only reduces high pledges

73When there is over-pledging (∑bi> PP), every backer individually has the incentive to lower

their pledge under all cases.

105

4.4. RESULTS

(bi>¯

b) but does not impact low pledges (bi≤¯

b), while the proportional rebate

rule reduces all pledges above the reservation price (bi> r), we arrive at our third

hypothesis.

Hypothesis 3: The variance of payments will be smaller under the bid-cap rule

than under the proportional rebate rule.

This Hypothesis requires that pledging behavior is not too different between the two

rebate rules. A possible behavioral conjecture would be that the bid-cap rule induces

higher pledges among those who try to guarantee the realization of the project and

lower pledges among free-riders, i.e., those who try to maximize their own payoff

with little regard for the realization of the project. In this case, dependent on the

pledging behavior, this could either cause a lower, similar, or even higher variance of

payments under the bid-cap rule compared with the proportional rebate rule. Yet,

there is no theoretical reason or empirical evidence indicating that pledging behavior

is different between the bid-cap and proportional rebate rules.

4.4 Results

In Table 4.1, we show summary statistics by experimental treatment, divided by

Part 1 and Part 2. On average, the pledges are greater than the efficient equilibrium

prediction of 30 under both rebate rules and below 30 under all-or-nothing. Demand

revelation is below 1 in all treatments. By design, the mean payments are exactly

30 under both rebate rules. Under all-or-nothing, around 1

/3of the projects were

funded, while more than 3

/4of the projects were funded under either rebate rule.

Overall, results are very similar between both parts of the experiment.

We provide an overview of general pledging tendencies in Figure 4.2 where we

classify by pledges below the reservation price, pledges above the reservation price

and below the mean equilibrium pledge of 30, which we consider free riding, pledges

within the mean equilibrium pledge of 30 and the valuation, which we consider

contributions, and pledges strictly above the valuation.74 Notably, under the all-

or-nothing treatment we find the most instances of pledges below the reservation

price.75 Under the bid-cap rule, we find the least instances of free riding and the

most contributions. Lastly, under the proportional rebate rule, we find considerably

more pledges above the valuation and the smallest share of contributions.

74See Figure 4.4 for the cumulative distribution and kernel density estimation of pledges.

75In all treatments pledges of bi= 0 account for around 3

/4of pledges bi<15.

106

4.4. RESULTS

All-or-nothing Proportional rebate Bid-cap

Part 1:

Mean pledge bi28 33.75a33.08

(13.91) (14.00) (13.48)

Demand revelation bi/vi0.62b0.75b0.74b

(0.27) (0.31) (0.30)

Payment when project funded 31.2 30 30

(10.69) ( 10.07) (6.54)

Proportion of projects funded 0.25 0.75 0.75

Part 2:

Mean pledge bi27.84 35.77a33.63a

( 14.07) (17.12) (14.41)

Demand revelation bi/vi0.63b0.82b0.77b

(0.30) (0.40) (0.35)

Payment when project funded 32.56 30 30

(13.28) ( 12.23) (9.28)

Proportion of projects funded 0.35 0.88 0.85

aSignificantly different from equilibrium prediction of 30.

bPledges are significantly different from valuation.

Table 4.1: Summary statistics with standard deviations in brackets.

In Figure 4.3, we show a mapping from pledges to payments for both rebate

rule treatments. We also add fitted predictions based on our observations. To fit

the proportional rebate treatment, we ran a regression of payments on pledges for

pledges bi∈[15,65] with suppressed constant term to determine the slope, while

payments are equal to the pledges for bi<15 by design of the rebate rules. To fit

the bid-cap treatment, we calculated the mean bid-cap ¯

bfor funded projects. This

constant is the payment for every pledge bi≥¯

b, while payments are equal to the

pledges for bi<¯

bby design of the rule.

Based on Spearman’s rank correlation coefficients, we find that pledges are cor-

related with the drawn valuations in all experimental treatments; all-or-nothing:

Spearman’s rho = 0.42,p < 0.001; proportional rebate: Spearman’s rho = 0.34,

p < 0.001; bid-cap: Spearman’s rho = 0.29,p < 0.001. As indicated by demand

revelations below one and despite these correlations, we find that participants pledge

significantly below their valuation in all experimental treatments and both parts of

the experiment, as seen in Table 4.4 in the Appendix. There we run the same regres-

sions as before, albeit normalizing the pledges at the individual valuation instead of

the mean equilibrium pledges. This result contrasts the findings of Rondeau et al.

(1999) and Spencer et al. (2009), who find demand revelation close to one, i.e., that

pledges were equal to valuations, in threshold public good settings. A potential

107

4.4. RESULTS

0.08

0.17

0.13

0.47

0.50

0.57

0.43

0.32

0.25

0.03

0.00

0.05

bi < 15 bi ∈ [15,30) bi ∈ [30,vi ] bi > vi

All-or-nothing

Proportional rebate

Bid-cap

Part 1

0.05

0.27

0.14

0.51

0.38

0.59

0.32

0.30

0.21

0.12

0.05 0.06

bi < 15 bi ∈ [15,30) bi ∈ [30,vi ] bi > vi

All-or-nothing

Proportional rebate

Bid-cap

Part 2

Figure 4.2: Distribution of pledges (classified).

reason for this difference is that Rondeau et al. (1999) and Spencer et al. (2009)

did not provide information on the exact provision point but only on the distribu-

tion it is drawn from. In Table 4.3 in the Appendix, we normalize the pledges to

the equilibrium prediction by subtracting 30 from each pledge and run regressions

on the constant remainder. We find that participants pledge on average less than

in equilibrium under the all-or-nothing treatment in both parts of our experiment,

yet this difference does not reach statistical significance at conventional levels. In

contrast, under both rebate rules, participants pledge more on average than in equi-

librium in both parts of the experiment. This is highly significant for Part 2 under

the proportional rebate rule.

Next, we test for treatment effects on pledges. We show the results in the first

two columns of Table 4.2. For Part 1, we run an OLS regression with robust stan-

dard errors, and for Part 2, we run random-effects regressions with standard errors

clustered on the subject level. For both parts of our experiment, we find that pledges

are significantly greater under both rebate rules compared with the all-or-nothing

model, while there is no significant difference between the two rebate rules.76 Given

these results, we can confirm our first Hypothesis.

Result 1: Pledges are larger under any rebate rule treatment compared with the all-

or-nothing treatment.

Similarly, in the third column of Table 4.2, we show the result of a random-effects

76The results hold when pooling Part 1 and Part 2 (see Table 4.6 in the Appendix).

108

4.4. RESULTS

Payment

5 15 25 35 45 55 65

Pledge

Proportional rebate

Fitted prediction

Bid-cap

Fitted prediction

Part 1

Payment

5 15 25 35 45 55 65

Pledge

Proportional rebate

Fitted prediction

Bid-cap

Fitted prediction

Part 2

Figure 4.3: Pledge to payment mapping of funded projects in rebate rule treatments.

regression with standard errors clustered on the group level on project realization

rates with the inclusion of treatment dummies. We find that projects were signifi-

cantly more likely to be funded under either rebate rule, while there is no significant

difference between rebate rule treatments in the project realization rate.77 This con-

firms our second Hypothesis.

Result 2: Project realization rates are larger under any rebate rule treatment com-

pared with the all-or-nothing treatment.

Part 1 (One round) Part 2 (Ten rounds)

bi∈[0,65] bi∈[0,65] Funded ∈ {0,1}

Proportional 5.88∗7.89∗∗∗ 0.53∗∗

(3.019) (2.593) (0.207)

Bid-cap 4.99∗5.67∗∗ 0.50∗∗

(2.994) (2.593) (0.217)

Constant 19.24∗∗ 15.53∗∗ 0.35∗

(8.548) (7.428) (0.188)

Level of observations Subject Subject Group

Number of observations 120 1200 120

Postestimation Wald tests to compare proportional rebate and bid-cap treatments:

H0: Proportional rebate =bid-cap p= 0.78 p= 0.44 p= 0.86

Standard errors in parentheses. Estimation by OLS regression with robust standard errors for Part 1 and esti-

mation by random-effects regression with clustering on level of observations for Part 2. The baseline category is

All-or-nothing in all specifications. ∗,∗∗ and ∗∗∗ denote significance at the 10%, 5% and 1% level, respectively.

Table 4.2: Analysis of treatment effects on pledges and the successful realization of projects.

77In Part 1, one out of four projects was funded under the all-or-nothing treatment, while three

out of four projects were funded under each rebate rule, respectively. Pooling Part 1 & Part 2 in

the estimations does not change the results (see Table 4.6 in the Appendix).

109

4.4. RESULTS

These findings contrast Marks and Croson (1998), who found no difference in

contributions and project realization rates between no rebates and proportional

rebates in a threshold public good setting. The most notable difference between their

experiment and ours is that they provided feedback between rounds, introducing

reputation effects and punishment opportunities. Moreover, we find consistency in

our results as we introduce another rebate rule next to the proportional rebate in

the form of the bid-cap.

Lastly, we compare the pledging patterns and payments for funded projects be-

tween the two rebate rule treatments. In Figure 4.5 in the Appendix, we show the

cumulative distribution of pledges and payments for funded projects.78 We begin by

considering Part 1. Using Kolmogorov-Smirnov tests, we find that there is no sig-

nificant difference in distributions of pledges of funded projects between rebate rule

treatments, D(60) = 0.267,p= 0.236, but a significant difference in distributions

of payments of funded projects between rebate rule treatments, D(60) = 0.500,

p < 0.001. In contrast, when considering Part 2, we find that between rebate

rules, there is a significant difference in distributions of pledges of funded projects,

D(690) = 0.162,p < 0.001, and a significant difference in distributions of payments

of funded projects, D(690) = 0.282,p < 0.001.

Similarly, using variance-comparison tests between rebate rules for Part 1, we

find that there is no significant difference in the standard deviation of pledges of

funded projects, F(29,29) = 1.286,p= 0.503 (two-sided F-Test), while the standard

deviation of payments of funded projects is significantly lower under the bid-cap

rule compared with the proportional rebate rule, F(29,29) = 2.372,p= 0.023 (two-

sided F-test). Again, when considering Part 2, we find both a significant difference

in the standard deviation of pledges of funded projects, F(349,339) = 1.495,p <

0.001 (two-sided F-Test), and a significant difference in the standard deviation of

payments of funded projects, F(349,339) = 1.736,p < 0.001 (two-sided F-Test).

Albeit the caveat that pledging patterns are different between the rebate rule

treatments in Part 2 of our experiment, we find a lower variance of payments under

the bid-cap rule compared with the proportional rebate rule in Part 1 and Part 2.

Therefore, we can confirm our third Hypothesis.

Result 3: The variance of payments is smaller under the bid-cap treatment com-

pared with the proportional rebate treatment.

78In Figure 4.6 in the Appendix, we show according kernel density estimations of pledges and

payments for funded projects.

110

4.5. CONCLUSION

4.5 Conclusion

In this study, we derive two rebate rules for reward-based crowdfunding, namely the

bid-cap rule and proportional rebate rule, and compare their theoretical properties

to each other and the widely applied all-or-nothing model. Both rebate rules benefit

backers whenever the sum of pledges strictly exceeds the provision point, which has

to be met for project realization, compared with the all-or-nothing model.

Applying all three rules in a laboratory experiment, we find that under both

rebate rules, pledges and the project realization rate are greater than under the

all-or-nothing. In line with its theoretical properties, we observe that the bid-cap

rule induces less variance of payments compared with the proportional rebate rule.

Compared with the proportional rebate rule, those who pledge the most pay less

under the bid-cap rule, while in contrast to the proportional rebate rule, those who

pledge the least do not receive a rebate under the bid-cap rule.

Since projects are realized more often if the excess pledges are rebated, it seems

advisable for crowdfunding platforms to offer some variation of a rebate rule. How-

ever, we cannot give definite guidance on which rebate rule to implement. We

observed more pledges above the valuation under the proportional rebate rule. A

potential reason might be that participants misinterpreted the proportional rebate

rule and erroneously tried to wager on high rebates, even though this could not in-

crease gains and might, in fact, even lead to losses.79 Hence, the proportional rebate

rule might be preferred by project creators but not by the crowdfunding platform

and project backers since it might induce over-pledging. On the other hand, the bid-

cap rule might be preferred by project backers concerned about fairness in terms

of payments since payments exhibit less variance under the bid-cap rule. In direct

comparison, our results slightly favor the bid-cap rule over the proportional rebate

rule.

A caveat to our findings is that on crowdfunding platforms, project creators

can endogenously determine the provision point and reservation price. The creators

might increase the provision point when they offer rebate rules as they cannot keep

the excess pledges. Whether the positive effects of rebate rules still prevail when the

provision point, reservation price, or both are chosen endogenously is an interesting

question for future research.

Furthermore, we focus on cases where the provision point cannot be met when

all individuals pledge the reservation price, yielding a residual public good game.

79Even though we checked comprehension of the instructions via control questions and asked

if people had any further questions, we cannot rule out that participants still misinterpreted the

rebate rules and their resulting payoffs.

111

4.5. CONCLUSION

For future research, one could extend the present study by introducing uncertainty

in the number of individuals who participate in the crowdfunding game, such that

it is unclear whether a residual public good game arise. Uncertainty in the number

of backers is equivalent to an uncertain provision point, as in Rondeau et al. (1999)

and Spencer et al. (2009). It would be interesting to test whether the bid-cap rule

extends to this situation similar to the proportional rebate rule in that demand

revelation increases. Also, in line with most crowdfunding applications, the rules

could be extended to allow for different tiers of rewards. Lastly, the efficacy of rebate

rules could be tested in field experiments using actual crowdfunding services.

112

4.6. APPENDIX

4.6 Appendix

4.6.1 Proof of negative marginal penalty of over-contribution

For the marginal penalty to be negative, it remains to be shown that the denominator is

greater than the numerator since then the second term in the first case will be strictly

smaller than one, i.e.,

(∑ei)2>(∑bi−PP)(∑ei−ei)+ei(∑ei).(4.7)

Rearranging yields:

∑ei>∑bi−PP. (4.8)

To see this inequality holds under the assumptions when the project is funded consider

that there are n∈(0, N]backers who pledge at least rand N−nwho pledge strictly

less than r80. In the following, we refer to the set of backers who pledge at least ras

I={all isuch that bi≥r}and use this to express ∑eiin terms of pledges bi:

∑ei=∑

i∈I

(bi−r).(4.9)

Plugging this into (4.8) and rearranging yields

PP > ∑

i∈I

bi+n·r. (4.10)

The RHS is bounded from above by N·r. Since we consider the case where N·r < PP,

the inequality is satisfied.81

4.6.2 Proof that a solution for the bid-cap rule must exist

The bid-cap rule determines a solution of the form (k,¯

b)for the following equation:

PP =

∑

i=1

bi+ (N−k)¯

b, (4.11)

where bk≤¯

b<bk+1 and k∈ {0, . . . , N −1}. We arrive there by starting with ∑bi> PP

and introducing the slack variable S > 0to turn the inequality into an equality:

∑bi−S=PP. (4.12)

80Note, that due to the assumption N·r < PP there needs to be at least one backer who

pledges more than rif the project is realized.

81If N·r > PP, this result must not necessarily hold. When ∑i∈Ir+∑i/∈Ibi> PP , the

marginal penalty will be positive and individuals would choose infinitely large pledges.

113

4.6. APPENDIX

We can set (4.12) equal to (4.11):

∑bi−S=

∑

i=1

bi+ (N−k)¯

b. (4.13)

We substitute S=∑N

i=k+1 si:

∑

i=k+1

bi−

∑

i=k+1

si= (N−k)¯

b⇐⇒

∑

i=k+1

(bi−si) = (N−k)¯

b. (4.14)

We can represent (4.14) with the definitions of Sand ¯

bas a system of equations:

∑

i=k+1

si=S

bk+1 −sk+1 =¯

. . .

bN−sN=¯

bk+1 >¯

bk≤¯

(4.15)

We continue to show that a solution to this system of equations must exist. Note that we

only consider cases where ∑bi> PP . Consider the upper interval limit k=N−1. The

system of equations reduces to bN−S=¯

band ¯

b≥bN−1. The highest contributor gets the

full rebate S. In the upper interval limit, the pledge of individual Nis required to realize

the project. Hence, 0< S ≤bN−bN−1, which implies that the inequalities above are

satisfied. Now consider the lower interval limit k= 0. Everyone gets a positive rebate and

pays exactly ¯

b. This is a solution as r≤¯

b < b1and S > ∑(bi−b1). We generalize this

observation to note that for any S > 0, we can find a kto solve the system of equations:

∃ksuch that

∑

i=k+1

(bi−bk+1)< S ≤

∑

i=k+1

(bi−bk)and bk≤¯

b<bk+1.(4.16)

This requires ∑N

i=k+1(bi−bk)>∑N

i=k+1(bi−bk+1)∀k, which holds as ∑N

i=k+1(bi−bk) =

∑N

i=k+1 bi−(N−k)·bk>∑N

i=k+1 bi−(N−k)bk+1 =∑N

i=k+1(bi−bk+1)since 0≤k≤N−1

and bk+1 > bkby definition. Now we express Sin terms of ¯

b, which is

∑

i=k+1

(bi−¯

b)(4.17)

114

4.6. APPENDIX

and notice that this does not violate (4.16), as bk≤¯

b<bk+1. As plugging (4.17) back

into (4.12) yields (4.11), a solution of the proposed form always exists as long as we have

∑bi> PP.

4.6.3 Proof that the solution in 4.6.2 is unique

We conduct our proof by contradiction. Consider a solution to (4.11) that we call (k,¯

following 4.6.2.

First suppose (k′,¯

b′)with k′< k and bk′≤¯

b′< bkis also a solution to (4.11).

The last inequality follows as we consider a situation in which decision maker kdoes not

cap out her pledge in contrast to (k,¯

b). However, (k′,¯

b′)cannot be a solution to (4.11) as

∑k′

i=1 bi+ (N−k′)¯

b′<∑k

i=1 bi+ (N−k)¯

b′<∑k

i=1 bi+ (N−k)bk≤∑k

i=1 bi+ (N−k)¯

Now assume (k′,¯

b′)with k′> k and ¯

b < bk+1 ≤¯

b′is a solution to (4.11). The

inequalities follow since as k′> k, we must have at least k′≥k+ 1, while ¯

b≤bk< bk+1

when under (k,¯

b)only consumers up to kcap out their pledges. Again, (k′,¯

b′)does not

solve (4.11) since ∑k′

i=1 bi+ (N−k′)¯

b′>∑k

i=1 bi+ (N−k)¯

b′≥∑k

i=1 bi+ (N−k)bk+1 >

∑k

i=1 bi+ (N−k)¯

4.6.4 Proof of payment relation of bid-cap and proportional

rebate for a discrete sequence of pledges

Consider a sequence of ordered pledges (b1, . . . , bN)with

∑bi> PP, (4.18)

where we, w.l.o.g., assume that b1> r. The sequence of final payments for all Nindividuals

under proportional rebate is given by:

(b1−e1·(∑bi−PP)

∑ei

, . . . , bN−eN·(∑bi−PP)

∑ei),(4.19)

where ei·(∑bi−PP)/∑eiare the individual rebates, which are weakly increasing, just

like the payments. Similarly, we denote the rebates and payments for all Nindividuals in

the bid-cap rule:

Rebate: ( 0, . . . , 0, bk+1 −¯

b,. . . ,bN−¯

b),

Payment: (b1,. . . ,bk,¯

b,. . . ,¯

b). (4.20)

All individuals from 1 to kwould be increasingly better off under the proportional rebate

rule since they receive no rebate under the bid-cap rule, while rebates under proportional

rebate increase proportionally with pledges. The difference in rebates is maximized when

bk=¯

b. Since under both rules, the sum of payments is equal to PP, the individuals from

115

4.6. APPENDIX

k+ 1 to Nwould receive the same total rebates under the bid-cap rule as all individuals

from 1to Nwould receive under the proportional rebate rule. Moreover, these N−k

individuals each pay the bid-cap ¯

b. Hence, the sum of payments by individuals from k+ 1

to Nmust be greater under the proportional rebate rule compared with the bid-cap rule.

We continue to show that we can construct a hypothetical intersection pledge ˆ

bwith

the property that people pledging more (less) than ˆ

bpay more (less) under the bid-cap

rule compared with the proportional rebate rule. To this end, consider the introduction of

an additional backer who pledges ˆ

b, which induces the same payment under both rebate

rules, i.e.,

b−(ˆ

b−r)·(∑bi+ˆ

b−PP −¯

∑ei+ (ˆ

b−r)=¯

b. (4.21)

Note that the introduction of ˆ

bmust leave the payment and rebate of all other individuals

unaffected. In order to have unaffected payments and rebates under the bid-cap rule, the

additional pledge ˆ

bneeds to correspond to a payment of ¯

band the provision point needs

to be increased by ¯

b. So that payments under proportional rebate are unaffected we must

have

bi−(bi−r)·(∑bi−PP)

∑ei

=bi−(bi−r)·(∑bi+ˆ

b−PP −¯

∑ei+ (ˆ

b−r)

⇐⇒ ∑bi−P P

∑ei

=ˆ

b−¯

b−r

.(4.22)

The introduction of this additional pledge and the increase of the provision point will

still lead to the provision of the good because by (4.21) it follows that ˆ

b > ¯

b⇒∑bi+ˆ

b >

PP +¯

b. By solving (4.22) for ˆ

band plugging it into (4.21), we can confirm that these

conditions hold for the proportional rebate rule, while it is immediate for the bid-cap rule,

since ˆ

bis strictly greater than ¯

bdue to (4.21). Further, we observe that any individual

i∈ {k+ 1, . . . , N}whose pledge is greater (smaller) than ˆ

bpays more (less) under the

bid-cap rule compared to the proportional rebate rule, indicating that ˆ

bis a (hypothetical)

intersection pledge.

116

4.6. APPENDIX

4.6.5 Additional regressions

Part 1 (One round) Part 2 (Ten rounds)

bi−30 bi−30 bi−30 bi−30 bi−30 bi−30

Constant -2.00 3.75∗3.08 -2.16 5.77∗∗∗ 3.63∗

(1.950) (2.213) (2.131) (1.706) (2.106) (1.862)

Treatment All-or-

nothing

Proportional

rebate Bid-cap All-or-

nothing

Proportional

rebate Bid-cap

Observations 40 40 40 400 400 400

Standard errors in parentheses. Estimation by OLS regression with robust standard errors for

Part 1 and estimation by random-effects regression with clustering on subject level for Part 2.

∗,∗∗ and ∗∗∗ denote significance at the 10%, 5% and 1% level, respectively.

Table 4.3: Analysis of pledges compared to the equilibrium prediction within experimental treat-

ments.

Part 1 (One round) Part 2 (Ten rounds)

bi−vibi−vibi−vibi−vibi−vibi−vi

Constant -17.00∗∗∗ -11.25∗∗∗ -11.93∗∗∗ -16.18∗∗∗ -8.25∗∗∗ -10.83∗∗∗

(1.950) (2.213) (2.131) (1.644) (2.134) (1.962)

Treatment All-or-

nothing

Proportional

rebate Bid-cap All-or-

nothing

Proportional

rebate Bid-cap

Observations 40 40 40 400 400 400

Standard errors in parentheses. Estimation by OLS regression with robust standard errors for

Part 1 and estimation by random-effects regression with clustering on subject level for Part 2.

∗,∗∗ and ∗∗∗ denote significance at the 10%, 5% and 1% level, respectively.

Table 4.4: Analysis of pledges compared to valuation within experimental treatments.

117

4.6. APPENDIX

Part 1 & Part 2 pooled

(Eleven rounds)

Part 1 & Part 2 pooled

(Eleven rounds)

bi−30 bi−30 bi−30 bi−vibi−vibi−vi

Constant -2.14 5.59∗∗∗ 3.58∗∗ -16.25∗∗∗ -8.52∗∗∗ -10.93∗∗∗

(1.628) (2.031) (1.811) (1.577) (2.056) (1.905)

Treatment All-or-

nothing

Proportional

rebate Bid-cap All-or-

nothing

Proportional

rebate Bid-cap

Observations 440 440 440 440 440 440

Standard errors in parentheses. Estimation by OLS regression with robust standard errors for

Part 1 and estimation by random-effects regression with clustering on subject level for Part 2.

∗,∗∗ and ∗∗∗ denote significance at the 10%, 5% and 1% level, respectively.

Table 4.5: Analysis of pledges compared to the equilibrium prediction and the valuation within

experimental treatments with Part 1 & Part 2 pooled.

Part 1 & Part 2 pooled

(Eleven rounds)

bi∈[0,65] Funded ∈ {0,1}

Proportional 7.73∗∗∗ 0.52∗∗

(2.583) (0.211)

Bid-cap 5.72∗∗ 0.50∗∗

(2.416) (0.221)

Constant 27.86∗∗∗ 0.34∗

(1.615) (0.186)

Level of observations Subject Group

Number of observations 1320 132

Postestimation Wald tests to compare rebate treatments:

H0: Proportional rebate =bid-cap p= 0.46 p= 0.88

Standard errors in parentheses. Estimation by OLS regression with random-effects regression

with clustering on level of observations. The baseline category is All-or-nothing in all specifica-

tions. ∗,∗∗ and ∗∗∗ denote significance at the 10%, 5% and 1% level, respectively.

Table 4.6: Analysis of treatment effects on pledges and the realization of projects with Part 1 &

Part 2 pooled

118

4.6. APPENDIX

4.6.6 Additional figures

5 15 25 35 45 55 65

All-or-nothing

Proportional rebate

Bid-cap

Part 1

5 15 25 35 45 55 65

All-or-nothing

Proportional rebate

Bid-cap

Part 2

.01

.02

.03

.04

.05

.06

.07

5 15 25 35 45 55 65

All-or-nothing

Proportional rebate

Bid-cap

Part 1

.01

.02

.03

.04

.05

.06

.07

5 15 25 35 45 55 65

All-or-nothing

Proportional rebate

Bid-cap

Part 2

Figure 4.4: Cumulative distribution of pledges (top) and kernel density estimation of pledges

(bottom) by experimental treatment.

119

4.6. APPENDIX

5 15 25 35 45 55 65

Proportional rebate

Bid-cap

Part 1

5 15 25 35 45 55 65

Proportional rebate

Bid-cap

Part 2

5 15 25 35 45 55 65

Proportional rebate

Bid-cap

Part 1

5 15 25 35 45 55 65

Proportional rebate

Bid-cap

Part 2

Figure 4.5: Cumulative distribution of pledges (top) and payments (bottom) of funded projects by

experimental treatment (only rebate rule treatments).

120

4.6. APPENDIX

.01

.02

.03

.04

.05

.06

.07

5 15 25 35 45 55 65

Proportional rebate

Bid-cap

Part 1

.01

.02

.03

.04

.05

.06

.07

5 15 25 35 45 55 65

Proportional rebate

Bid-cap

Part 2

.01

.02

.03

.04

.05

.06

.07

5 15 25 35 45 55 65

Proportional rebate

Bid-cap

Part 1

.01

.02

.03

.04

.05

.06

.07

5 15 25 35 45 55 65

Proportional rebate

Bid-cap

Part 2

Figure 4.6: Kernel density of pledges (top) and payments (bottom) of funded projects by experi-

mental treatment (only rebate rule treatments).

121

4.6. APPENDIX

4.6.7 Translated instructions

[Original instructions were in German. Expressions in square brackets were not visible to

participants]

Instructions [All experimental treatments]

Welcome to this experiment and thank you for your participation! This experiment begins

now. Please read these instructions carefully. The instructions are identical for all partici-

pants present. If you have any questions, please raise your hand and an experimenter will

come by to you to answer your questions. If the question that you have asked should be

relevant to everybody, then we will repeat the questions for all and provide a response.

Please do not communicate with other participants during the experiment and please turn

off your mobile phones now. This is an experiment on decision-making. You can earn

money in this experiment which depends on your decisions and the decisions of the other

participants. The amount you earn will be paid out to you in cash after the experiment.

In beginning, you will be randomly assigned to a group consisting of you and ten other

participants. This group remains the same and does not change throughout the experi-

ment. You will make your decisions privately and not learn who the other group members

are.

This experiment consists of two parts. You can find the instructions for the first part

below. You will receive instructions for part two after the first part is over.

All monetary values in this experiment are denominated in Experimental Currency Units

(ECU). Your total earnings is the sum of the payoff you earned in part 1 and in part 2

which will be exchanged at a rate of 10 ECU = 0,40 Euro at the end of the experiment.

In addition, independent of your earnings, you receive 6 Euros for your participation.

Part 1 [All-or-nothing treatment]

Your task in the first Part:

In the beginning, you and your group members will be assigned one of two roles (ac-

tive/passive) with there being ten active group members and one passive group member

in each group.

You and your other group members each are given 65 ECU to start independently from

your role. The active group members can invest any amount out of the given endow-

ment into a project which will only be realized if the total investment costs of 300 ECU

122

4.6. APPENDIX

are reached. The passive group member cannot invest into the project. Your payoff in

the first part depends on whether you are an active or passive group member and the

decisions of the active group members.

Every active group member can become an investor of the project. To be considered an

investor of the project, an active group member needs to make a minimum investment

of at least 15 ECU. Investments below 15 ECU are just seen as a donation and do not

entitle a participant to a payout.

If the total group investments are below the investment costs of 300 ECU, the investment

put forward by active group members is returned and they do no receive a payout from

the project, neither does the passive member. All active and passive members receive

their endowment.

If your group’s total investment is at least 300 ECU and meets the investment costs, each

active group member’s investment that is below 15 ECU is considered as a donation and

these members do not receive a payout from the project. They just receive the remaining

amount of their endowment, which they have not invested. Every investor receives a

payout of 45 ECU, and their remaining amount of the endowment, which they have not

invested. The passive group member also receives a payout of 45 ECU in addition to the

initial endowment. If your group’s total investment is above 300 ECU, the passive group

member additionally receives the excess investments.

Example

Participant A B C D E F G H I J K

Role active passive

Investments 0 7 14 21 28 35 42 49 56 63 -

Based on these investments D, E, F, G, H, I, and J are investors as they invested above

15 ECU whereas A, B and C are not. Consequently, the investments of A, B and C are

merely considered donations. After subtracting the donations of A, B and C 0+7+14=

21 ECU from the investment costs of 300 ECU, only 279 ECU are needed in order

to realize the project. The remaining investments are enough to cover 279 ECU, as

28 + 35 + 42 + 49 + 56 + 63 = 294. This results in additional excess investments of

294 −279 = 15 ECU which are paid out to the passive participant K.

123

4.6. APPENDIX

Summary of potential earnings for active group members

•If the investment cost are not reached, the active group member receives:

earnings =endowment

•If the investment costs are exactly covered but the active group member invested less

than the minimum required to become an investor, then the investment is considered

a donation:

earnings =endowment −donation

•If the investment costs are covered and the active group member invested at least

the minimum required to become an investor, the paid amount is determined by:

earnings =endowment +payout −investments

Summary of potential earnings for passive group members

•If the investment cost are not reached, the passive group member receives:

earnings =endowment

•If the investment costs are exactly covered the passive group member receives:

earnings =endowment +payout

•If the overall investments made by the group exceed the investment costs the passive

group member receives:

earnings =endowment +payout +excess investments

If you have questions with regard to Part 1, please raise your hand and an experimenter

will come by and answer your question.

Part 1 [Proportional rebate treatment]

Your task in the first Part:

In the beginning, you and your group members will be assigned one of two roles (ac-

tive/passive) with there being ten active group members and one passive group member

in each group.

You and your other group members each are given 65 ECU to start independently from

your role. The active group members can invest any amount out of the given endow-

ment into a project which will only be realized if the total investment costs of 300 ECU

are reached. The passive group member cannot invest into the project. Your payoff in

the first part depends on whether you are an active or passive group member and the

decisions of the active group members.

124

4.6. APPENDIX

Every active group member can become an investor of the project. To be considered an

investor of the project, an active group member needs to make a minimum investment

of at least 15 ECU. Investments below 15 ECU are just seen as a donation and do not

entitle a participant to a payout.

If the total group investments are below the investment costs of 300 ECU, the investment

put forward by active group members is returned and they do no receive a payout from

the project, neither does the passive member. All active and passive members receive

their endowment.

If your group’s total investment is at least 300 ECU and meets the investment costs, each

active group member’s investment that is below 15 ECU is considered as a donation and

these members do not receive a payout from the project. They just receive the remaining

amount of their endowment, which they have not invested. Every investor receives a

payout of 45 ECU, and the remaining amount of their endowment, which they have not

invested. The passive group member also receives a payout of 45 ECU in addition to

the initial endowment.

If your group invests more than the required investment costs of 300 EC, then each in-

vestor receives a share of the excess investments. The rebate of the excess investments is

made according to the following rule:

Firstly, it is determined for each investor how much more than the minimum investment

of 15 ECU each of them has invested. The difference between the investment and min-

imum investment is called contribution. The share out of the excess investments each

investor gets, is directly proportional to each investor’s share of the sum of contributions.

For instance, if an investor is responsible for a quarter of the total contributions then this

investor receives a quarter of the excess investments.

This means investors pay at most their investment and potentially less if the entirety of

their investment is not needed in order to cover the investment costs. This also means

that investors with higher investments potentially receive higher rebates. Investors only

pay their entire investment if needed to realize the project. We refer to the part of the

investment actually used to realize the project – i.e. what an investor ultimately pays for

the realization of the project – as the paid amount. The following example illustrates

this rule in more detail.

125

4.6. APPENDIX

Example

Participant A B C D E F G H I J K

Role active passive

Investments 0 7 14 21 28 35 42 49 56 63 -

Based on these investments D, E, F, G, H, I, and J are Investors whereas A, B and C are

not. Consequently, the investments of A, B and C are merely considered donations. After

subtracting the donations of A, B and C 0 + 7 + 14 = 21 ECU from the investment costs,

only 279 ECU are needed in order to realize the project. The remaining investments are

enough to cover 279 ECU, as 28 + 35 + 42 + 49 + 56 + 63 = 294. So 294 −279 = 15

ECU will be contributed as excess investments, which will be returned proportionally to

the investor contributions. Below you will find the calculation of the contributions and

rebates of all investors:

The minimum investment in order to become an investor is 15 ECU and D invests 21

ECU. D’s contribution is then 21 −15 = 6 ECU. E’s contribution is 28-15=13 ECU,

F’s contribution is 35-15=20 ECU, G’s contribution is 42-15=27 ECU, H’s contribution

is 49-15=34 ECU,I’s is 56-15=41 ECU und J’s is 63-15=48 ECU. The sum of all contri-

butions is then 6+13+20+27+34+41+48=189 ECU.

D’s contribution is 6 ECU and the sum of all contributions is 189 ECU. So D’s share of

the contributions is 6

/189. This portion of the contributions is multiplied by the excess

investment of 15 ECU to determine the rebate.

Consequently, D receives a rebate of 6

/189 ·15= 0.48 ECU. Equivalently, E receives a

rebate of 13

/189 ·15 = 1.13 ECU, F a rebate of 20

/189 ·15 = 1.59 ECU, G a rebate of

/189 ·15 = 3.14 ECU, H a rebate of 34

/189 ·15 = 2.7ECU, I a rebate of 41

/189 ·15 = 3.25

ECU and J a rebate of 48

/189 ·15 = 3.81 ECU.

In the table below you can see the investments and the paid amounts made by all investors.

Participant A B C D E F G H I J K

Role active passive

Investment 0 7 14 21 28 35 42 49 56 63 -

Paid Amount 0 7 14 20.52 26.97 33.41 39.86 46.30 52.75 59.19 -

126

4.6. APPENDIX

Summary of potential earnings for active group members

•If the investment cost are not reached, the active group member receives:

earnings =endowment

•If the investment costs are exactly covered but the active group member invested less

than the minimum required to become an investor, then the investment is considered

a donation:

earnings =endowment −donation

•If the investment costs are covered and the active group member invested at least

the minimum required to become an investor, the paid amount is determined by:

earnings =endowment +payout −paid amount

Summary of potential earnings for passive group members

•If the investment cost are not reached, the passive group member receives:

earnings =endowment

•If the investment costs are exactly covered the passive group member receives:

earnings =endowment +payout

•If the overall investments made by the group exceed the investment costs the passive

group member receives:

earnings =endowment +payout

If you have questions with regard to Part 1, please raise your hand and an experimenter

will come by and answer your question.

Part 1 [Bid-cap treatment]

Your task in the first Part:

In the beginning, you and your group members will be assigned one of two roles (ac-

tive/passive) with there being ten active group members and one passive group member

in each group.

You and your other group members each are given 65 ECU to start independently from

your role. The active group members can invest any amount out of the given endow-

ment into a project which will only be realized if the total investment costs of 300 ECU

are reached. The passive group member cannot invest into the project. Your payoff in

the first part depends on whether you are an active or passive group member and the

decisions of the active group members.

127

4.6. APPENDIX

Every active group member can become an investor of the project. To be considered an

investor of the project, an active group member needs to make a minimum investment

of at least 15 ECU. Investments below 15 ECU are just seen as a donation and do not

entitle a participant to a payout.

If the total group investments are below the investment costs of 300 ECU, the investment

put forward by active group members is returned and they do no receive a payout from

the project, neither does the passive member. All active and passive members receive

their endowment. If your group’s total investment is at least 300 ECU, each active group

member’s investment that is below 15 ECU is considered as a donation and these members

do not receive a payout from the project. They just receive the remaining amount of their

endowment, which they have not invested. Every investor receives a payout of 45 ECU,

and the remaining amount of their endowment, which they have not invested. The pas-

sive group member also receives a payout of 45 ECU in addition to the initial endowment.

If your group invests more than the required investment costs, then each investor receives

a share of the excess investments. The rebate of the excess investments is made according

to the following rule:

Firstly, the donations of active group members that invested less than 15 ECU are sub-

tracted from the investment costs. Then it is checked whether the investment costs minus

the donations would be reached if each investor contributes the lowest investment that has

been made. If this is the case, then each investor pays the lowest investment and the excess

investments are distributed equally between all investors.

If this is not the case, then the investor(s) who made the lowest investment, pay the lowest

investment and it is checked again whether the investment cost minus the donations is

reached if all other investors pay the second-highest investment. If this is the case, then

the investor(s) with the lowest investment contribute the lowest investment and all other

investors contribute the second-lowest investment. The excess investments are distributed

equally between investors that paid the second-lowest investment. This process continues

until the lowest possible investment is found for which the investment costs minus the

donations are reached.

The investors pay at most their investment and potentially less if the entirety of their

investment is not needed in order to cover the investment costs. This also means that

investors with higher investments potentially receive higher rebates. Overall, the investors

only pay their entire investment only if needed. We refer to the part of the investment

actually used to realize the project – i.e. what an investor ultimately pays for the realization

of the project – as the paid amount. The following example illustrates this rule in more

detail:

128

4.6. APPENDIX

Example

Investor A B C D E F G H I J

Investment 0 7 14 21 28 35 42 49 56 63

Based on these investments D, E, F, G, H, I, J are Investors whereas A, B and C are not.

Consequently, the investments of A, B and C are merely considered as donations. After

subtracting the donations of A, B and C 0 + 7 + 14 = 21 ECU from the investment costs,

only 279 ECU are needed in order to realized the project.

Now it is checked whether 279 ECU can be covered if all investors make the lowest in-

vestment of 21 ECU. As 21 ·7 = 147 <279, this does not cover the costs. D pays 21

ECU and it is checked whether 279 ECU can be covered if all other investors E ,F ,G ,H,

I, J each make the second-lowest investment of 28 ECU. As 6·28 + 21 = 189 <279 the

costs are not covered. In the next iteration, D pays 21 ECU und E pays 28 ECU and it is

checked whether 279 ECU can be covered if all other investors each make the third-lowest

investment of 35 ECU which results in 21 + 28 + 5 ·35 = 224 <279.

This process continues until Investor Iis reached. In this case, all investors pay their

invested amounts and I and J pay 56 ECU each. This results in total investments of

21+28+35+42+49+2·56 = 287 ECU which covers the investment cost minus the

donations. Therefore, J receives a rebate of 63−56 = 7 ECU, as J’s investment is reduced

to I’s investment.

In addition, these investments lead to excess investments of 287 −279 = 8 ECU. These 8

ECU are now distributed equally among investors I and J, so that I and J each receive a

rebate of 4ECU.

In the end, all investors pay their investments except for I and J, who pay less than their

investments as their entire investment is not needed to cover the investment costs. I’s paid

amount is 56 −4 = 52 ECU, since I receives a rebate out of the excess investments. J’s

paid amount is 63−7−4 = 52 ECU, since J’s investment is reduced to I’s investment and

J receives a rebate out of the excess investments.

The following table summarizes the investments and the paid amounts for all investors.

Participant A B C D E F G H I J K

Role active passive

Investment 0 7 14 21 28 35 42 49 56 63 -

Paid Amount 0 7 14 21 28 35 42 49 52 52 -

129

4.6. APPENDIX

Summary of potential earnings for active group members

•If the investment cost are not reached, the active group member receives:

earnings =endowment

•If the investment costs are exactly covered but the active group member invested less

than the minimum required to become an investor, then the investment is considered

a donation:

earnings =endowment −donation

•If the investment costs are covered and the active group member invested at least

the minimum required to become an investor, the paid amount is determined by:

earnings =endowment +payout −paid amount

Summary of potential earnings for passive group members

•If the investment cost are not reached, the passive group member receives:

earnings =endowment

•If the investment costs are exactly covered the passive group member receives:

earnings =endowment +payout

•If the overall investments made by the group exceed the investment costs the passive

group member receives:

earnings =endowment +payout

If you have questions with regard to Part 1, please raise your hand and an experimenter

will come by and answer your question.

Part 2 [All experimental treatments]

The second part of the experiment begins now. In this part, you will be repeating the task

from Part 1 ten times. Your role is identical to the first part. In each round, you will

receive a starting capital of 65 ECU. The payout each active group member can get

(in ECU) will be determined independently for each active group member at the begin-

ning of every round through a random draw from the interval [30,60]. Each number in

the interval is equally likely to be drawn and each active group member will receive their

individual number independently of other active player numbers. The potential payout for

the passive group member in every round is 45 ECU as in the first part. You will neither

get feedback about the investments that other active group members made in previous

rounds nor whether the investment costs were reached.

130

4.6. APPENDIX

In this part overall, group members and roles, the investment costs, starting capital, the

minimum investment in order to become an investor and the rule concerning excess invest-

ments are the same. At the beginning of each round, active group members will learn

their randomly drawn payout as an investor and decide how much to invest into the project.

The potential earnings in each round are determined the exact same way as in the first

part of the experiment. Active group members receive their investment back in case the

project is not successfully realized. Passive group members also receive their investment

back in case the project is not successfully realized. The earnings equal the start capital

minus the investment if the project is realized but the active group member invested less

than 15 ECU. If the investment costs are covered and an active group member invested

at least 15 ECU, then they receive their randomly drawn payout in addition to the starting

capital, minus the paid amount, which is determined following the same rule as in part 1.

[Proportional rebate treatment/Bid-cap treatment]

If the project is realized in a round, a passive group member receives the endowment and

their payout from the project.

[All-or-nothing treatment]

If the project is realized in a round, a passive group member receives the endowment,

their payout from the project and any excess investment.

[All experimental treatments]

The overall payoff from Part 2 equals the payoff you have received in a randomly drawn

round. Hereby, each round is equally likely to be drawn. Your earnings in this part will

be exchanged at a rate of 10 ECU = 0,40 Euro.

Since you do not know which round is relevant for your payment of the second part, it is

optimal for you to decide as if each round determines your payment.

In case you have any questions with regard to Part 2 please raise your hand and an

experimenter will come by to you to answer your questions. If the question that you have

asked should be relevant to everybody, then we will repeat the questions for all and provide

a response.

131

Chapter 5

Concluding Remarks

This dissertation consists of three contributions that combine theoretical and experimen-

tal methods to address novelties rooted in the digital economy, explicitly privacy, data

protection, and crowdfunding. Chapter 2 deals with experimental methods and the limits

to theory-testing in behavior-based pricing experiments. The findings of Chapter 2 are

relevant in Chapter 3, which theoretically and experimentally explores the impact of data

protection regulations on competitive markets. Chapter 4 veers away from predictions

that are purely informed by game theoretic equilibria and instead relies on differences in

the cases off the equilibrium path. While this posits an impasse for pure theorists, it

demonstrates the complementarity of theoretical and experimental methods.

In the first contribution, I examine whether findings of experimental studies on behavior-

based pricing can be replicated and evaluate why observed prices deviate from point pre-

dictions. I report observed prices in conformity with point predictions through a uniform

pricing benchmark, a replication of a behavior-based pricing experiment, and a follow-up

experiment in which I implement the second period disjointed from the first period. By dis-

joining the two periods, I show that reference dependence toward first-period prices shifts

the second-period pricing behavior of participants upwards. Further, I show that con-

sidering consumers myopic instead of strategic explains a downward shift of first-period

prices and rationalizes prior experimental findings that did not replicate in my experiment.

Lastly, I show that price-based welfare measures are prone to distortions when pricing de-

cisions are biased. Transport costs are a suitable alternative that alleviates this issue. In a

subsequent contribution, we study a duopoly model of behavior-based pricing where con-

sumers decide whether they reveal their data or remain anonymous by contrasting two data

policies. In an open data policy, revealed data is accessible by both sellers in the market.

As a result, all consumers reveal their data in a unique equilibrium, while firm-side price

132

discrimination causes (total) welfare losses due to poaching. In an exclusive data policy,

revealed data is only accessible by the one firm a consumer bought from. Thus, consumers’

equilibrium decision is to anonymize, leading to uniform prices and efficient markets. We

test these contrasting predictions in a laboratory experiment. We find that in the open

data treatment, subjects predominantly act as predicted. In contrast, in the exclusive data

treatment, buyers initially reveal their data as sellers reward loyalty. Subsequently, buyers

adjust more towards anonymization, when sellers begin to employ poaching strategies. Our

results show that, given the freedom of choice, consumers use their privacy right to their

benefit under an open data policy, but to their detriment under an exclusive data policy.

For the final contribution we turn from (online) consumer privacy to another

digitization-enabled setting – the creator economy. Explicitly, we study the efficacy of

rebate rules in reward-based crowdfunding, i.e., a form of crowdfunding where a project is

realized when a collective of backers contributes a sufficient amount of pledges such that

a pre-set funding goal is met. We introduce a novel rebate rule, which sets a cap on pay-

ments toward the project. Any pledges above this cap are reduced to it. This bid-cap rule

has similar properties as the proportional rebate rule, which originated in the threshold

public goods literature. Under both rebate rules, pledges are reduced such that the sum

of payments exactly equals the funding goal. However, in contrast to the bid-cap rule, the

proportional rebate rule achieves this by reducing all pledges instead of only the highest.

In an experiment, we can confirm that both rebate rules incentivize backers to pledge

higher amounts, which leads to an increased project success rate. Moreover, when viewing

fairness just in terms of final payments, we find that the bid-cap rule is preferable when

implementing rebates as it benefits those who pledge the most while not rebating anything

to those who pledge the least.

While the issues discussed in this dissertation may warrant further inspection by fu-

ture research, new issues surrounding the digital economy are already emerging. Whereas

privacy and data protection – and to some extent the creator economy – have been one of

the major concerns in the economic literature of the 2010s, as of this writing, signs point at

artificial intelligence filling a similar pivotal role in the 2020s. Interdisciplinary approaches,

both within and between fields, will become relevant once again as, in a similar fashion

to privacy concerns and data protection, artificial intelligence will be relevant throughout

many scientific areas, including political science, social science, psychology, philosophy,

computer science, and – last but not least – economics.

133

Bibliography

Ackley, G. (1942). Spatial competition in a discontinuous market. The Quarterly Journal

of Economics, 56(2):212–230.

Acquisti, A. (2008). Identity management, privacy, and price discrimination. IEEE Security

& Privacy, 6(2):46–50.

Acquisti, A. and Grossklags, J. (2005). Privacy and rationality in individual decision

making. IEEE security & privacy, 3(1):26–33.

Acquisti, A., John, L. K., and Loewenstein, G. (2013). What is privacy worth? The

Journal of Legal Studies, 42(2):249–274.

Acquisti, A., Taylor, C., and Wagman, L. (2016). The economics of privacy. Journal of

Economic Literature, 54(2):442–92.

Acquisti, A. and Varian, H. R. (2005). Conditioning prices on purchase history. Marketing

Science, 24(3):367–381.

Agrawal, A., Catalini, C., and Goldfarb, A. (2014). Some simple economics of crowdfund-

ing. Innovation policy and the economy, 14(1):63–97.

Ali, S. N., Lewis, G., and Vasserman, S. (2019). Voluntary disclosure and personalized

pricing. Technical report, National Bureau of Economic Research.

Anderson, S. P., Baik, A., and Larson, N. (2019). Price discrimination in the information

age: Prices, poaching, and privacy with personalized targeted discounts.

Ansink, E., Koetse, M. J., Bouma, J., Hauck, D., and van Soest, D. (2017). Crowdfunding

public goods: An experiment.

134

BIBLIOGRAPHY

Armstrong, M. (2006a). Recent developments in the economics of price discrimination.

Armstrong, M. (2006b). Recent developments in the economics of price discrimination.

Cambridge University Press.

Asplund, M., Eriksson, R., and Strand, N. (2008). Price discrimination in oligopoly:

evidence from regional newspapers. The Journal of Industrial Economics, 56(2):333–

346.

Banerjee, A. (1987). On frequent flyer programs and other loyalty-inducing economic ar-

rangements. Harvard University.

Barreda-Tarrazona, I., García-Gallego, A., Georgantzís, N., Andaluz-Funcia, J., and Gil-

Sanz, A. (2011). An experiment on spatial competition with endogenous pricing. Inter-

national Journal of Industrial Organization, 29(1):74–83.

Baye, I. and Sapi, G. (2014). Targeted pricing, consumer myopia and investment in

customer-tracking technology. Number 131. DICE Discussion Paper.

Belleflamme, P. and Vergote, W. (2016). Monopoly price discrimination and privacy: The

hidden cost of hiding. Economics Letters, 149:141–144.

Beresford, A. R., Kübler, D., and Preibusch, S. (2012). Unwillingness to pay for privacy:

A field experiment. Economics Letters, 117(1):25–27.

Bourreau, M. and De Streel, A. (2018). The regulation of personalised pricing in the digital

era.

Brokesova, Z., Deck, C., and Peliova, J. (2014a). Experimenting with purchase history

based price discrimination. International Journal of Industrial Organization, 37:229–

237.

Brokesova, Z., Deck, C., and Peliova, J. (2014b). Experimenting with purchase history

based price discrimination. International Journal of Industrial Organization, 37:229–

237.

Camacho-Cuena, E., García-Gallego, A., Georgantzís, N., and Sabater-Grande, G. (2005).

Buyer–seller interaction in experimental spatial markets. Regional Science and Urban

Economics, 35(2):89–108.

Caminal, R. and Matutes, C. (1990). Endogenous switching costs in a duopoly model.

International Journal of Industrial Organization, 8(3):353–373.

Capponi, G., Corrocher, N., and Zirulia, L. (2021). Personalized pricing for customer re-

tention: Theory and evidence from mobile communication. Telecommunications Policy,

45(1):102069.

135

BIBLIOGRAPHY

Carroni, E. et al. (2015). Competitive behaviour-based price discrimination among asym-

metric firms. CERPE.

Casadesus-Masanell, R. and Hervas-Drane, A. (2015). Competing with privacy. Manage-

ment Science, 61(1):229–246.

Cason, T. N., Tabarrok, A., and Zubrickas, R. (2021). Early refund bonuses increase

successful crowdfunding. Games and Economic Behavior, 129:78–95.

Cason, T. N. and Zubrickas, R. (2017). Enhancing fundraising with refund bonuses. Games

and Economic Behavior, 101:218–233.

Cason, T. N. and Zubrickas, R. (2019). Donation-based crowdfunding with refund bonuses.

European Economic Review, 119:452–471.

Chemla, G. and Tinn, K. (2020). Learning through crowdfunding. Management Science,

66(5):1783–1801.

Chen, Y. and Pearcy, J. (2010). Dynamic pricing: when to entice brand switching and

when to reward consumer loyalty. The RAND Journal of Economics, 41(4):674–685.

Choe, C., Cong, J., and Wang, C. (2023). Softening competition through unilateral sharing

of customer data. Management Science.

Choe, C., King, S., and Matsushima, N. (2018). Pricing with cookies: Behavior-based

price discrimination and spatial competition. Management Science, 64(12):5669–5687.

Choe, C., Matsushima, N., and Tremblay, M. J. (2022). Behavior-based personalized

pricing: When firms can share customer information. International Journal of Industrial

Organization, 82:102846.

Choi, J. P., Jeon, D.-S., and Kim, B.-C. (2019). Privacy and personal data collection with

information externalities. Journal of Public Economics, 173:113–124.

Chopin, N. (2011). Fast simulation of truncated gaussian distributions. Statistics and

Computing, 21(2):275–288.

Coats, J. C., Gronberg, T. J., and Grosskopf, B. (2009). Simultaneous versus sequential

public good provision and the role of refunds—an experimental study. Journal of Public

Economics, 93(1-2):326–335.

Colombo, S. (2016). Imperfect behavior-based price discrimination. Journal of Economics

& Management Strategy, 25(3):563–583.

Comeig, I., Mesa-Vázquez, E., Sendra-Pons, P., and Urbano, A. (2020). Rational herding

in reward-based crowdfunding: An mturk experiment. Sustainability, 12(23):9827.

136

BIBLIOGRAPHY

Conitzer, V., Taylor, C. R., and Wagman, L. (2012). Hide and seek: Costly consumer

privacy in a market with repeat purchases. Marketing Science, 31(2):277–292.

Corazzini, L., Cotton, C., and Valbonesi, P. (2015). Donor coordination in project fund-

ing: Evidence from a threshold public goods experiment. Journal of Public Economics,

128:16–29.

Cornelius, P. B. and Gokpinar, B. (2020). The role of customer investor involvement in

crowdfunding success. Management Science, 66(1):452–472.

Cosguner, K., Chan, T. Y., and Seetharaman, P. (2017). Behavioral price discrimination

in the presence of switching costs. Marketing Science, 36(3):426–435.

Croson, R. T. and Marks, M. B. (2000). Step returns in threshold public goods: A meta-and

experimental analysis. Experimental Economics, 2(3):239–259.

Cumming, D. J., Leboeuf, G., and Schwienbacher, A. (2020). Crowdfunding models: Keep-

it-all vs. all-or-nothing. Financial Management, 49(2):331–360.

De Nijs, R. (2017). Behavior-based price discrimination and customer information sharing.

International Journal of Industrial Organization, 50:319–334.

Deb, J., Oery, A., and Williams, K. R. (2019). Aiming for the goal: Contribution dynamics

of crowdfunding. Technical report, National Bureau of Economic Research.

Dinev, T. and Hart, P. (2006). An extended privacy calculus model for e-commerce trans-

actions. Information Systems Research, 17(1):61–80.

Dufwenberg, M., Sundaram, R., and Butler, D. J. (2010). Epiphany in the game of 21.

Journal of Economic Behavior & Organization, 75(2):132–143.

Esteves, R.-B. (2014). Price discrimination with private and imperfect information. The

Scandinavian Journal of Economics, 116(3):766–796.

Esteves, R.-B. (2022). Can personalized pricing be a winning strategy in oligopolistic

markets with heterogeneous demand customers? yes, it can. International Journal of

Industrial Organization, 85:102874.

Esteves, R. B. and Cerqueira, S. (2017). Behavior-based pricing under imperfectly informed

consumers. NIPE Working Paper Series, 3:1–33.

Esteves, R. B. et al. (2009). A survey on the economics of behaviour-based price discrimi-

nation. Technical report, NIPE-Universidade do Minho.

Fischbacher, U. (2007a). z-tree: Zurich toolbox for ready-made economic experiments.

Experimental economics, 10(2):171–178.

137

BIBLIOGRAPHY

Fischbacher, U. (2007b). z-tree: Zurich toolbox for ready-made economic experiments.

Experimental Economics, 10(2):171–178.

Fool, T. M. (2023). The largest companies by market cap in 2023. https://www.fool.

com/research/largest-companies-by-market-cap/. [accessed 24-May-2023].

Fudenberg, D. and Tirole, J. (2000). Customer poaching and brand switching. RAND

Journal of Economics, pages 634–657.

Fudenberg, D. and Villas-Boas, J. M. (2006a). Behavior-based price discrimination and

customer recognition. Handbook on economics and information systems, 1:377–436.

Fudenberg, D. and Villas-Boas, J. M. (2006b). Behavior-based price discrimination and

customer recognition. Handbook on Economics and Information Systems, 1:377–436.

Garella, P. G., Laussel, D., and Resende, J. (2021). Behavior based price personalization

under vertical product differentiation. International Journal of Industrial Organization,

76:102717.

Gerber, E. M. and Hui, J. (2013). Crowdfunding: Motivations and deterrents for partici-

pation. ACM Transactions on Computer-Human Interaction (TOCHI), 20(6):1–32.

Ghosh, A., Mahdian, M., McAfee, R. P., and Vassilvitskii, S. (2015). To match or not

to match: Economics of cookie matching in online advertising. ACM Transactions on

Economics and Computation (TEAC), 3(2):1–18.

Gneezy, U., Rustichini, A., and Vostroknutov, A. (2010). Experience and insight in the

race game. Journal of Economic Behavior & Organization, 75(2):144–155.

Greiner, B. (2015a). Subject pool recruitment procedures: organizing experiments with

orsee. Journal of the Economic Science Association, 1(1):114–125.

Greiner, B. (2015b). Subject pool recruitment procedures: Organizing experiments with

orsee. Journal of the Economic Science Association, 1(1):114–125.

Hotelling, H. (1929). Stability in competition. The Economic Journal, 39(153):41–57.

Isaac, R. M., Schmidtz, D., and Walker, J. M. (1989). The assurance problem in a labora-

tory market. Public choice, 62(3):217–236.

Laussel, D. and Resende, J. (2022). When is product personalization profit-enhancing? a

behavior-based discrimination model. Management Science, 68(12):8872–8888.

Li, G. and Wang, J. (2019). Threshold effects on backer motivations in reward-based

crowdfunding. Journal of Management Information Systems, 36(2):546–573.

138

BIBLIOGRAPHY

Li, K. J. and Jain, S. (2016). Behavior-based pricing: An analysis of the impact of peer-

induced fairness. Management Science, 62(9):2705–2721.

Li, X., Li, K. J., and Wang, X. (2020). Transparency of behavior-based pricing. Journal

of Marketing Research, 57(1):78–99.

Liu, Q. and Serfes, K. (2004). Quality of information and oligopolistic price discrimination.

Journal of Economics & Management Strategy, 13(4):671–702.

Loertscher, S. and Marx, L. M. (2020). Digital monopolies: Privacy protection or price

regulation? International Journal of Industrial Organization, page 102623.

Mahmood, A. (2014a). How do customer characteristics impact behavior-based price dis-

crimination? an experimental investigation. Journal of Strategic Marketing, 22(6):530–

547.

Mahmood, A. (2014b). How do customer characteristics impact behavior-based price dis-

crimination? an experimental investigation. Journal of Strategic Marketing, 22(6):530–

547.

Mahmood, A. and Vulkan, N. (2018). Do small firms pay to stay? an experimental

investigation. Journal of Marketing Behavior, 3(2):121–152.

Malhotra, N. K., Kim, S. S., and Agarwal, J. (2004). Internet users’ information privacy

concerns (iuipc): The construct, the scale, and a causal model. Information Systems

Research, 15(4):336–355.

Marks, M. and Croson, R. (1998). Alternative rebate rules in the provision of a threshold

public good: An experimental investigation. Journal of public Economics, 67(2):195–

220.

Mikians, J., Gyarmati, L., Erramilli, V., and Laoutaris, N. (2012). Detecting price and

search discrimination on the internet. In Proceedings of the 11th ACM workshop on hot

topics in networks, pages 79–84.

Mikians, J., Gyarmati, L., Erramilli, V., and Laoutaris, N. (2013). Crowd-assisted search

for price discrimination in e-commerce: First results. In Proceedings of the ninth ACM

Conference on Emerging Networking Experiments and Technologies, pages 1–6.

Montes, R., Sand-Zantman, W., and Valletti, T. (2018). The value of personal information

in online markets with endogenous privacy. Management Science.

Norberg, P. A., Horne, D. R., and Horne, D. A. (2007). The privacy paradox: Per-

sonal information disclosure intentions versus behaviors. Journal of consumer affairs,

41(1):100–126.

139

BIBLIOGRAPHY

Palfrey, T. R. and Rosenthal, H. (1984). Participation and the provision of discrete public

goods: a strategic analysis. Journal of public Economics, 24(2):171–193.

Parliament and Council of the European Union (2016). Regulation (eu) 2016/679. http:

//data.europa.eu/eli/reg/2016/679/oj.

Preibusch, S., Kübler, D., and Beresford, A. R. (2013). Price versus privacy: An experi-

ment into the competitive advantage of collecting less personal information. Electronic

Commerce Research, 13(4):423–455.

Regner, T. and Crosetto, P. (2018). It’s never too late: Funding dynamics and self pledges

in reward-based crowdfunding. Research Policy, 47(8):1463–1477.

Regner, T. and Crosetto, P. (2021). The experience matters: participation-related rewards

increase the success chances of crowdfunding campaigns. Economics of Innovation and

New Technology, 30(8):843–856.

Rhodes, A. and Zhou, J. (2021). Personalized pricing and privacy choice. Technical report,

Working paper.

Robert, C. P. (1995). Simulation of truncated normal variables. Statistics and computing,

5(2):121–125.

Rondeau, D., Schulze, W. D., and Poe, G. L. (1999). Voluntary revelation of the demand for

public goods using a provision point mechanism. Journal of public Economics, 72(3):455–

470.

Schudy, S. and Utikal, V. (2017). You must not know about me–on the willingness to share

personal data. Journal of Economic Behavior & Organization, 141:1–13.

Shen, Q. and Miguel Villas-Boas, J. (2018). Behavior-based advertising. Management

Science, 64(5):2047–2064.

Shilony, Y. (1977). Mixed pricing in oligopoly. Journal of Economic Theory, 14(2):373–388.

Shin, J. and Sudhir, K. (2010). A customer management dilemma: When is it profitable

to reward one’s own customers? Marketing Science, 29(4):671–689.

Smith, V. L. (1980). Experiments with a decentralized mechanism for public good decisions.

The American Economic Review, 70(4):584–599.

Solomon, J., Ma, W., and Wash, R. (2015). Don’t wait! how timing affects coordination

of crowdfunding donations. In Proceedings of the 18th acm conference on computer

supported cooperative work & social computing, pages 547–556.

140

BIBLIOGRAPHY

Spencer, M. A., Swallow, S. K., Shogren, J. F., and List, J. A. (2009). Rebate rules in

threshold public good provision. Journal of Public Economics, 93(5-6):798–806.

Statista (2021). Market size of crowdfunding worldwide in 2020 with

a forecast for 2027. https://www.statista.com/statistics/1078273/

global-crowdfunding-market-size/. [accessed 30-July-2022].

Strausz, R. (2017). A theory of crowdfunding: A mechanism design approach with demand

uncertainty and moral hazard. American Economic Review, 107(6):1430–76.

Streitfeld, David (2000). On the web, price tags blur. https://www.washingtonpost.

com/archive/politics/2000/09/27/on-the-web-price-tags-blur/

14daea51-3a64-488f-8e6b-c1a3654773da.

Taylor, C. R. (2004). Consumer privacy and the market for customer information. RAND

Journal of Economics, pages 631–650.

Tsai, J. Y., Egelman, S., Cranor, L., and Acquisti, A. (2011). The effect of online pri-

vacy information on purchasing behavior: An experimental study. Information Systems

Research, 22(2):254–268.

Umezawa, M. (2022). Behavior-based price discrimination in a horizontally and verti-

cally differentiated duopoly with switching costs. Information Economics and Policy,

61:101004.

Voss, W. G. and Houser, K. A. (2019). Personal data and the gdpr: providing a competitive

advantage for us companies. American Business Law Journal, 56(2):287–344.

Wash, R. and Solomon, J. (2014). Coordinating donors on crowdfunding websites. In

Proceedings of the 17th ACM conference on Computer supported cooperative work &

social computing, pages 38–48.

Xu, Y. and Ni, J. (2022). Entrepreneurial learning and disincentives in crowdfunding

markets. Management Science, 68(9):6819–6864.

141