Of coordinators and dictators: A public goods experiment

Fleiß, Jürgen; Palan, Stefan Article Of coordinators and dictators: A public goods experiment Games Provided in Cooperation with: MDPI – Multidisciplinary Digital Publishing Institute, Basel Suggested Citation: Fleiß, Jürgen; Palan, Stefan (2013) : Of coordinators and dictators: A public goods experiment, Games, ISSN 2073-4336, MDPI, Basel, Vol. 4, Iss. 4, pp. 584-607, https://doi.org/10.3390/g4040584 This Version is available at: https://hdl.handle.net/10419/98513 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. http://creativecommons.org/licenses/by/3.0/ Games 2013,4, 584-607; doi:10.3390/g4040584 OPEN ACCESS games ISSN 2073-4336 www.mdpi.com/journal/games Article Of Coordinators and Dictators: A Public Goods Experiment J¨ urgen Fleiß 1and Stefan Palan 2,3,* 1Institute of Statistics and Operations Research, University of Graz, Universit¨ atsstrasse 15, 8010 Graz, Austria; E-Mail: juer[email protected] 2Department of Banking and Finance, University of Innsbruck, Universit¨ atsstrasse 15, 6020 Innsbruck, Austria 3Institute of Banking and Finance, University of Graz, Universit¨ atsstrasse 15/F2, 8010 Graz, Austria *Author to whom correspondence should be addressed; E-Mail: [email protected]; Tel.: +43-512-507-7564; Fax: +43-512-507-2846. Received: 17 July 2013; in revised form: 11 September 2013 / Accepted: 8 October 2013 / Published: 10 October 2013 Abstract: We experimentally investigate whether human subjects are willing to give up individual freedom in return for the benefits of improved coordination. We conduct a modified iterated public goods game in which subjects in each period first decide which of two groups to join. One group employs a voluntary contribution mechanism, the other group an allocator contribution mechanism. The setup of the allocator mechanism differs between two treatments. In the coordinator treatment, the randomly selected allocator can set a uniform contribution for all group members, including herself. In the dictator treatment, the allocator can choose different contributions for herself and all other group members. We find that subjects willingly submit to authority in both treatments, even when competing with a voluntary contribution mechanism. The allocator groups achieve high contribution levels in both treatments. Keywords: allocator; public goods game; self-selection, institution choice, power In 2005, a special issue of Science listed the 25 areas where scientists perceived the most important gaps in our knowledge to date [1]. These included the question, raised by Pennisi [2], of how cooperative behavior evolved to form the basis for the complex societal structures we observe today. She pointed out the importance of investigating which conditions and institutional settings promote cooperation in situations where individuals have an incentive not to cooperate. A famous example of such a dilemma is Games 2013,4585 of course the contribution to a public good. In the standard setting, individuals have strong incentives to maximize their own payoffs by free riding and not contributing to the public good. As a result, a group of rational actors would be unable to supply a public good. A large number of laboratory experiments have investigated cooperation in the public goods game (for reviews, see [3,4]). In the most common version of the repeatedly played public goods game, each individual in a group makes his or her own decision about how much of the endowment to contribute to a public good in every period. The results show that contributions tend to start out at an average of around 50% and decline towards zero [4,5]. Looking at individual behavior, a number of subjects are usually found to contribute in the first few periods of repeated public goods games. Over time, their contributions decline as they observe other subjects free riding and contributing nothing. In the end, because of these conditional cooperators’ reactions to the free riders, the public good no longer gets produced [6–8]. These somewhat disappointing findings on human cooperative behavior in such dilemmas have been qualified by more recent results. There are mechanisms that can foster contributions to the public good. One such solution is monetary punishment, as introduced by Ostrom, Gardner and Walker [9]. Their paper, and a number of follow-up studies, show that (centralized and decentralized) punishment and reward can stabilize contributions at high levels [10–13].1Besides punishment, voting on the implementation of different proposed contribution rules has been shown to have a positive effect [14,15]. We claim that besides the instruments of punishment and reward, direct power over the decisions of others can play an important role when it comes to the success of collective action in dilemma situations. Weber [16] defines power as “the likelihood that one person in a social relationship will be able, even despite resistance, to carry out his own will.” Structures of (asymmetric) power distributions are omnipresent in everyday life and characterize whole societies, but also groups, (business) organizations and the like [16,17]. Yet, despite its obvious importance in everyday life, the discipline of economics has not devoted much time to studying power over the decisions of others (for an analogous argument and another recent experimental study regarding power, see [18]). Kroll et al. [19] show that contributions to a public good increase if group members in a public goods game can vote for a binding proposal as opposed to making voluntary contributions. One particularly noteworthy recent exception builds on the idea of binding subjects to specific actions. It employs a new contribution mechanism in public good games, based on an asymmetric distribution of power: the allocator mechanism. The two studies introducing this topic are Hamman et al. [20] and Bolle and Vogel [21]. Both show that, under certain conditions, one way of promoting the provision of a public good is to establish an allocator who has absolute power over the decisions of all group members. In the unique rational expectations equilibrium, this allocator is then able to force all group members to contribute their full endowment to the public good, thereby maximizing the collective outcome. Hamman et al. [20] and Bolle and Vogel [21] largely confirm this theoretical prediction and show experimentally that the use of an allocator results in comparatively very high contributions to the public good. Where the two studies differ is in the specifics of group members’ and allocators’ choice sets and in the structure of the experiment. Hamman et al. [20] let group members elect an allocator and find that groups 1For a recent review, see [4]. Games 2013,4586 ensure full provision of the public good primarily by electing pro-social allocators. Since each group of nine holds a new election every period, their setting allows for punishment by removing underperforming allocators from power. Allocators who contribute fully for everyone are found to be re-elected in almost all cases. Bolle and Vogel [21] choose a different first phase for their experiment. They initially let subjects play 10 periods of a public goods game with voluntary contributions. This is followed by one period, where an allocator is chosen (either randomly or by election) to make the allocation decision for the two other members of her three-person group. This sequence of voluntary (10 periods) and allocator contribution phases (one period) is repeated twice, such that subjects play three allocator periods in total. Like Hamman et al. [20], Bolle and Vogel [21] observe higher contributions in the allocator setting than in the setting with voluntary contributions. Interestingly, they find no statistically significant differences between the election and the random selection treatments. The great success of the allocator mechanism documented in these two studies merits further research. We explore its performance characteristics by (i) systematically varying the action space of the allocator and by (ii) studying whether subjects prefer groups governed by the allocator mechanism over groups where they can freely choose their own contribution when group choice is endogenous. Note that the two precursor studies implement the allocator mechanism in a way that either forces all subjects to participate or allows endogenous participation, such that non-participating subjects profit from the public good of participating subjects. In this second case, Hamman et al. [20] find that the allocator mechanism is not able to increase contributions due to free riding. Only when communication is possible do half of their groups choose to transfer their decision rights and achieve high contribution levels. We build on these results and investigate whether the transformation of the public good into a club good, from which only group members can profit, is also able to foster the allocator mechanism’s efficiency. Our second question therefore is of special importance, since it captures a subject’s willingness to submit to authority for her own benefit and the benefit of the whole group. This question is also closely related to a major finding in the discipline of new institutional economics [22]. It states that the voluntary participation of subjects in finding a solution to coordination problems substantially increases the likelihood of success. Such endogenous institution choice has previously also been examined for the punishment and reward mechanisms mentioned above. One approach is to let subjects vote whether they want to implement, e.g., punishment in the public goods game they will later be playing [23]. Another is to let subjects self-select into groups with different, exogenously fixed institutional settings. G¨ urerk et al. [24] find that subjects are more likely to self-select into groups with sanctioning institutions than into alternative groups and that the likelihood of choosing the group with sanctioning institution increases over time. In this way, they show that when two groups with different institutional settings compete against each other, the group with a sanctioning institution—due to the higher payoffs it generates for its members—prevails in the end. Hamman et al. [20] also present some of these aspects in their experiments. They allow subjects to choose whether they want to be part of electing an allocator who will then make the contribution decision on their behalf or whether they want to choose their level of contribution themselves. The important difference to the design of G¨ urerk et al. [24] (and this study) is that subjects who choose not to be part of the electoral delegation mechanism in Hamman et al. [20] nonetheless profit from the public goods contributions made by subjects who have delegated their decision power. This allows subjects Games 2013,4587 who have not joined the delegation mechanism to free ride on its outcomes.2Without communication, Hamman et al. [20] obtain an average contribution level of only 11%. In this setting, the allocator mechanism thus fails to sustain high public goods contributions. Whether groups governed by the allocator mechanism have an advantage over groups with voluntary contribution when one group does not profit from the contributions of the other is an important and unanswered question. Building on Hamman et al. [20] and Bolle and Vogel [21], we thus identify two important questions. First, do subjects prefer a group governed by the allocator mechanism over a group with a voluntary contribution mechanism? Second, which factors influence subjects’ group choice? The present article answers both of these questions. As an additional innovation, we drill down into the role played by the allocator’s action space. Specifically, we compare a treatment with what we term a coordinator—an allocator who can choose one uniform contribution level for all members of her group, including herself—to a treatment with a dictator—an allocator who can choose a contribution level for herself and a different, uniform contribution level for all other group members. This mimics many settings outside the lab where a group leader or government establishes policies that apply to all group members equally (e.g., regulations that require every able-bodied male adult to contribute to the public good of national defense by having to serve a term in the military, as exists in many countries). Consider as a loosely-related example for our setting a country’s decision to join the European Union. This country faces a tradeoff between giving up the freedom to decide on its laws and regulations entirely on its own and abdicating some of its regulatory authority to the EU institutions in return for the benefits from greater cooperation. This example shares with our design the feature that leadership of the group, in this case, the presidency of the council of the EU, rotates through all member states, with each country serving only one term. (Another example would be the decision by a stone-age human to join a tribe, thus giving up individual freedom in order to gain the ability to jointly hunt larger game, which is argued to have contributed to the rise of modern civilization; see, e.g., [26]). The remainder of this paper is structured as follows. In Section 1, we state our research questions and derive our hypotheses. Section 2outlines the experimental design and procedures. Results are presented in Section 3and discussed in Section 4. 1. Research Question and Hypotheses We investigate the question of how societal coordination can arise endogenously in response to economic coordination problems. We take a standard public good game as our workhorse model and augment it by giving subjects the freedom to select into one of two groups at the beginning of every period. In the voluntary contribution group (VCG), they play a standard public good game by deciding how much of their endowment to keep for themselves and how much to invest into a public good. If subjects select into the allocator contribution group (ACG), one group member is randomly chosen to set the contribution level for all ACG members. 2Kosfeld et al. [25] showed that centralized punishment institutions are able to prevail in a setting where non-participating players can free ride on the contributions of the players participating in the centralized punishment institution. This leads to high levels of efficiency in their public goods experiments. Games 2013,4588 Given a contribution level, we use the same payoff function in both groups. Specifically, a subject’s payoff for any one period in our experiment is calculated as follows:3 πi=Ei−ci+λ nθ · nθ X j=1 cθ j(1) where πiis the payoff of subject i,Ei=E= 20 is a subject’s endowment in each period in experimental currency units (ECU), ciis the subject’s contribution to the public good in this period, λ= 1.6is a constant determining the marginal per capita return (MPCR), nθis the number of subjects in group θ∈ {V CG, ACG}and Pnθ j=1 cθ jis the sum of all contributions of subjects jin group θin this period. The return from the public good is rendered independent of the group size through the inclusion of nθin the denominator of the MPCR. It thus depends only on the average contribution in the group (this follows the design of Rockenbach and Milinski [27]). In the special case that only a single subject selects into one of the groups, the subject’s contribution is automatically set to zero, and no public good is generated (subjects are so informed in the instructions). Note that subjects receive information about their group’s size before making their contribution decision. Figure 1. Treatment design and terminology. Coordinator Contribution Group CCG Allocator Contribution Group ACG Voluntary Contribution Group VCG Dictator Contribution Group DCG Coordinator Treatment: The allocator can set a uniform contribution level for all group members. The allocator (= randomly selected group member) decides on contributions of all group members. Treatments differ in the allocator action space. Dictator Treatment: The allocator can set a different contribution level for himself/herself. Hamman et al. [20] and Bolle and Vogel [21] implemented the allocator decision in a way that allowed the allocator to set a different contribution for herself than for the other group members. This allows for the rise of “corruption”, which is how we refer to the case where the allocator does not contribute to the public good.4Our design expands on this idea by modeling two different types of allocator decision options. We will continue to use “allocator” and ACG as the general terms, but will distinguish between a “coordinator” and a “dictator” treatment in our design. In the former, the coordinator can choose a contribution level, which then applies to all group members, including herself. In the latter, the dictator can choose two contribution levels, one of which applies to all group members excluding 3We suppress the period index in order to streamline the notation. 4Note that our instructions generally contained neutral wording, for example, referring to the VCG (ACG) as the “group with individual contribution choice” (“group with contribution choice by a randomly determined player”). Games 2013,4589 herself, while the other applies only to herself. In keeping with the vocabulary just laid out, we will be speaking of two forms of ACGs—the coordinator contribution group (CCG) and the dictator contribution group (DCG). Figure 1illustrates this terminology. Finally, we wish to explore the impact of subjects’ social preferences on their behavior in our experiment. For this reason, we elicit their social value orientation using the social value orientation (SVO) slider measure developed by Murphy et al. [28]. 1.1. Rational Expectations Predictions To predict the group choice, we have to take a look at the expected contributions and payoffs in each of the two groups. In the VCG, the rationally5expected behavior is not to contribute, yielding an expected payoff to every subject equal to her endowment. (This is also the minimax payoff in the VCG.) In the ACGs, there are different predictions for our two treatments. Given that the coordinator can only set one uniform contribution level for all group members, it is immediately apparent that for any λ > 1(and assuming E > 0), the profit-maximizing strategy is to set the contribution level equal to the common endowment, E. The payoff to both the coordinator and the other group members, then, is the payoff from full cooperation: πi,CCG =λ nCCG ·E·nCCG (2) Given that λ= 1.6and E= 20 in our setting, we thus derive the first part of our first hypothesis: Hypothesis 1a. In the CCG, coordinators always contribute the full endowment. In the coordinator treatment, the expected payoff as a member of the allocator group is higher6than the minimax payoff in the voluntary contribution group, which equals the endowment E.7Under rational expectations, we would therefore expect all subjects to choose the allocator group in the coordinator treatment despite their lack of knowledge, at the time of making the decision, of the subsequently resulting group size. We use this benchmark for the derivation of the second part of our first hypothesis: Hypothesis 1b. All subjects in the coordinator treatment select into the CCG. In the dictator treatment, we assert that a rational allocator would set the contribution of all group members equal to their endowments and set a contribution of zero for herself. This yields the following payoffs: πi,DCG =   E+λ nDCG ·E·(nDCG −1) if subject iis the dictator, and λ nDCG ·E·(nDCG −1) if subject iis not the dictator (3) We reflect the incentives induced by this payoff function in the first part of our second hypothesis. 5Note that rational in this case includes the assumption that the actors are only interested in maximizing their own payoff without regard for the payoff of others. 6Strictly speaking, this is only true if subjects assign a positive probability to nCCG >1. 7This result holds for any λ > 1and, thus, for any public good. Games 2013,4590 Hypothesis 2a. In the DCG, dictators always contribute nothing themselves and the full endowment for all other group members. Since every player who joins the DCG has a chance of 1nDCG to become the dictator, the conditionally expected payoff (assuming full contribution) of joining the DCG, given a group size of nDCG, would be: E[πi,DCG] = 1 nDCG ·E+λ nDCG ·E·(nDCG −1)(4) where Eis the conditional expectations operator assuming equilibrium play (i.e., full contribution in the ACG; no contribution in the VCG). It follows from Equations (2) and (4), as well as from our treatment of the special case of a group size of one that E[πi,DCG]≥E[πi,V CG],with E[πi,DCG] = E[πi,V CG]iff nDCG = 1. Thus, even though the resulting group sizes are as yet undetermined when subjects make their group choice, selecting into the VCG is nonetheless a dominant strategy. This is also the case for the worst possible outcome in the DCG when only two subjects join the DCG.8This leads to the second part of our second hypothesis: Hypothesis 2b. All subjects in the dictator treatment select into the DCG. Despite their theoretical validity, we judge it likely that hypotheses 1a and 1b, as well as hypotheses 2a and 2b will not hold in our experiments. Experimental economists (among others) have shown that people do not behave in an exclusively payoff maximizing manner. In our setting, possible reasons for off-equilibrium behavior include the heterogeneity of social preferences, bounded rationality, salience effects, aversion to risk and/or losses and a dislike of competing per se. Unfortunately, there is a large number of different theories of, e.g., social preferences, such that it is not possible to include all of them with precise predictions. We will therefore formulate some hypotheses regarding expected deviations from perfectly rational behavior based on social value orientation and inequality aversion. 1.2. Social Preference Predictions Social preference models (and also social value orientation) assume that individuals are not concerned about their own payoff alone, but also about the payoffs to others and the relative sizes of their own and others’ payoffs. One specific form of social preferences is inequality-aversion. Outcome based models of inequality aversion assume that subjects are averse to differences in outcomes (see, e.g., [29,30]). This allows us to make a prediction regarding the differences in group choice between the coordinator and dictator treatments. Since no inequality is possible in the CCG, inequality aversion cannot be a cause for subjects choosing the VCG in the coordinator treatment. This is different in our dictator treatment. Here, the dictator can choose different contribution levels for himself and for the other DCG members, thereby increasing his payoff relative to the other group members’. This reduces the utility of inequality-averse 8Following from Equation (4), this assertion implies the following inequality: 1nACG ·E+λnACG ·E·(nACG −1) > E. It is easy to show that it simplifies to λ > 1if E > 0and n > 1. Games 2013,4591 subjects and renders the VCG relatively more attractive to them.9Since we assume that there likely are such subjects in our subject pool, we reflect this in our next hypothesis: Hypothesis 3. Subjects are more likely to choose the ACG in the coordinator treatment than in the dictator treatment. Once we drop the assumption of rational expectations, subjects can be assumed to update their expectations of other participants’ behavior based on their observations of past outcomes. We expect an effect of the amount of the dictator contribution in the previous period on subjects’ group choice in the subsequent period. Hypothesis 4. Subjects’ likelihood of selecting into the DCG increases in the previous period’s dictator contribution. As Equation (3) makes clear, the negative effects of low dictator contributions in the DCG are diluted with increasing group size, since the cost of dictator free riding is jointly borne by more group members. We expect that this dilution effect will make it more likely for dictator treatment subjects to join the DCG when they expect many others to do so.10 Note, however, that our subjects do not know the group size for the period for which they are currently making their group choice. We conjecture that they will use the group size information from the previous period as a proxy for the current period’s DCG size when forming their expectations of the latter.11 Hypothesis 5. Subjects’ likelihood of selecting into the DCG increases in the previous period’s DCG size. We also explore the impact of allocators’ social value orientation on their decisions in the experiment. Subjects with a pro-social value orientation not only care about themselves, but also about relevant others (see, e.g., [31,32]). On the other hand, pro-self individuals are more interested in their own payoff. Previous experiments show that a pro-social value orientation correlates with cooperative behavior in economic experiments (see, e.g., [33]).12 On this basis, we expect pro-social dictators to set a higher contribution level for themselves than do pro-self dictators. In the CCG, pro-social and pro-self coordinators should behave the same way (setting the contribution of everyone equal to the endowment). Hypothesis 6. Pro-social dictators set their own contribution higher than pro-self dictators. 9Note that dictators with social preferences (like inequality-aversion or deriving positive utility from the payoffs of others) might themselves contribute (fully) to the public good (see hypothesis 6). We thank an anonymous referee for pointing this out. 10 Note that the dilution effect is counteracted by the decrease in probability of being assigned the dictator role with the attendant higher possible payoff. Refer to the Appendix in Section 4for a proof that the first effect outweighs the second. Strictly speaking, our argument is based on the net effect. 11 While we do consider this question to be interesting, we did not judge it important enough to explicitly elicit group size expectations, which carries a risk of causing an experimenter demand effect. 12 For a review, see [34]. Games 2013,4598 Figure 4. Overall trend in average group size over time in the two treatments. The figure displays the average group size in each of the ten periods separately for the dictator and the coordinator treatments. The data of rounds 1 and 2 are pooled. The dashed lines are linear predictions. The thin lines are average group sizes in individual sessions. 0 3 6 9 12 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 Coordinator Dictator ACG Group Size VCG Group Size Group Size Period Next, we conduct a regression analysis of the aggregate data, which is presented in Table 2. In the models (which we fit individually for each treatment), we control for the round, the period and the interaction between the two, allowing the slope of the periods to vary between rounds. We also include previous period data on the average size of, and the average contribution in, the ACG. Games 2013,4599 Table 2. Group size. The table shows the results of OLS regressions of the CCG and DCG group sizes on a number of regressors. Round is 1 (2) in the first (second) of the two 10-period sequences. Period2 equals the period number Period in round 2 and zero otherwise. The remaining variables are the lagged average contributions in the ACG and the lagged ACG group size (of the DCG in the regression of the dictator treatment, of the CCG in the analysis of the coordinator treatment) and the lagged contribution of the dictator in the DCG. Model 1 Model 2 Regressors CCG Group Size DCG Group Size Round 0.098 (0.538) 0.690 (0.516) Period 0.069 (0.071) 0.060 (0.056) Period2 0.041 (0.104) −0.078 (0.069) Lagged Average Contribution in ACG 0.103 (0.016) *** 0.089 (0.034) ** Lagged Dictator Contribution in DCG 0.033 (0.014) * Lagged Group Size in ACG 0.287 (0.157) 0.393 (0.059) *** Constant 4.537 (0.937) ** 2.942 (0.889) ** R20.30 0.37 Adjusted R20.25 0.34 N 72 117 *p<0.1; ** p<0.05; *** p<0.01. Standard errors clustered at the session level (in parentheses). Our results show that the time effect visible in Figure 4is not significant in either treatment when controlling for the variables that were identified as relevant in our hypotheses in Section 1. Models 1 and 2 share one statistically significant effect: a larger average ACG contribution in the previous round results in a larger current ACG group size, supporting our hypothesis 8. It also implies that when the allocator contributes relatively little, the group size of the VCG increases in the following period. Furthermore, for the dictator treatment only, we find a significant effect of the DCG group size in the previous period. This provides support for the presence of the dilution effect, as conjectured in hypothesis 5. Finally, we find a significant effect of the dictator contribution in the previous period on the DCG group size (hypothesis 4).16 We continue our analysis by investigating individual subjects’ group choice behavior using Probit models.17 Table 3presents the two regression models we believe best reflect the structural relationships in our data. In Model 3, we include the Round and Period variables, a treatment dummy and a variable containing our subjects’ social value orientation as measured using the instrument defined in Murphy et al. [28]. Higher values of the SVO measure indicate a greater willingness to give up own 16 Tobit regression censored at zero and 12 yields similar results. 17 Robustness checks confirm that our main results are stable with regard to the use of a logit model and to the inclusion or exclusion of different questionnaire items. A translation of the questions is provided in the Electronic Supplementary Information. Games 2013,4600 income to benefit others. We also include an interaction of SVO with the treatment dummy, as well as variables containing information on the previous period’s average contributions in the VCG and ACG (AvgContribVCG L and AvgContribACG L) and on the size of the ACG (and, separately, for the DCG) in the previous period (GroupSizeACG L and GroupSizeACG L x Dictator). Table 3. Determinants of allocator group choice. The table shows the results of Probit regressions of IsACG on a number of regressors. IsACG is a dummy equal to zero (one) if the subject chooses the VCG (ACG) in a period. Dictator is a dummy variable equal to zero (one) in the coordinator (dictator) treatment. Round is 1 (2) in the first (second) of the two 10period sequences. Period2 equals the period number Period in round 2 and zero otherwise. SVO is the social value orientation of the subjects, measured using the slider-measure from Murphy et al. (2011), and SVO x Dictator is SVO interacted with Dictator. The remaining variables are the lagged average contributions in the ACG and VCG, the lagged ACG group size (pooled and in the dictator treatment only) and the lagged contribution of the dictator in the dictator treatment (note that the model that includes this variable solely uses dictator treatment data). Logit estimation and logit panel regression yield similar results. Robustness checks, where we include various questionnaire response items and interaction terms, yield no clear effects from the control variables, but leave the main effects unchanged. Regressors Model 3 Model 4 Subsample All cases Dictator treatment Dictator −1.284 (0.679) * Round −0.127 (0.187) −0.012 (0.303) Period 0.000 (0.017) 0.008 (0.026) Period2 0.026 (0.027) 0.010 (0.041) SVO −0.010 (0.011) SVO x Dictator 0.020 (0.015) 0.010 (0.010) AvgContribACG L 0.030 (0.008) *** 0.024 (0.011) ** AvgContribVCG L −0.046 (0.012) *** −0.038 (0.012) *** GroupSizeACG L 0.044 (0.061) GroupSizeACG L x Dictator 0.085 (0.066) 0.119 (0.038) *** DictContrib L 0.009 (0.007) Constant 0.661 (0.594) −0.750 (0.475) Pseudo R20.04 0.04 N 1,358 746 *p<0.1; ** p<0.05; *** p<0.01. Standard errors clustered at the subject level (in parentheses). As predicted in hypothesis 3, we find a negative treatment effect. Subjects are less likely to join the ACG in the dictator treatment. Our model also shows that the likelihood of a subject selecting into the ACG as opposed to the VCG increases in the average contribution in the ACG in the previous period, thus lending further support to our hypothesis 8. Conversely, higher contributions in the VCG in the Games 2013,4601 previous period decrease the likelihood of subjects joining the ACG. This result supports hypothesis 7. We also find that greater social value orientation of a subject cannot be shown to play a role.18 Finally, the results do not yield any evidence of subjects being more likely to select into the ACG in later periods or in the second round. Model 4 differs from Model 3 in that it uses only the dictator treatment data and contains the amount of the previous period’s dictator contribution as an additional variable. We find a statistically significant effect of the lagged size of the DCG, but not the ACG in general, lending further support to the dilution effect of hypothesis 5. Model 4 also shows a significant effect of the lagged average contribution in the DCG, but none of the lagged dictator contribution. Hypothesis 4does not receive support from this result. The average contribution in the VCG in the previous period shows a highly significant negative coefficient, again, in line with our hypothesis 7. Just as in the pooled analysis, there appears not to be a material effect of SVO on group choice. 18 Two subjects did not fill in the SVO questionnaire correctly and are, therefore, excluded from all analyses employing social value orientation data. Furthermore, the session 11 data are not included, since no SVO or other questionnaire items were elicited, due to the server crash. Games 2013,4602 Table 4. Determinants of dictator contribution choice. The table shows the results of an OLS regression of the dictator’s own contribution on a number of regressors. Round is 1 (2) in the first (second) of the two 10-period sequences. Period2 equals the period number Period in round 2 and zero otherwise. SVO is the social value orientation of the dictator, measured using the slider-measure from Murphy et al. [28]. The remaining variables are the lagged average contribution in the DCG, the concurrent DCG group size and the lagged dictator contribution. The inclusion of the lagged variables leads to the exclusion of the observations from period 1 in rounds 1 and 2. Tobit regression censored at zero and 20 yields similar results. Robustness checks, where we include various questionnaire response items and interaction terms, yield no clear effects from the control variables, but leave the main effects unchanged. Regressors Model 5 Round −2.225 (4.214) Period −0.691 (0.454) Period2 0.417 (0.632) AvgContribDCG L −0.159 (0.266) GroupSizeDCG 0.736 (0.486) DictatorContribution L 0.325 (0.104) *** SVO 0.127 (0.060) ** Constant 5.132 (7.438) R20.23 Adj. R20.17 N 107 *p<0.1; ** p<0.05; *** p<0.01. Standard errors clustered at the subject level (in parentheses). Games 2013,4603 3.3. Contributions We next focus on dictators’ contribution behavior in the DCG. Table 4contains our OLS regression results for the dictator’s own contribution (Model 5). We control for a time trend, the lagged contributions, the group size of the ACG, the lagged dictator contribution and SVO. First, this is the only instance where we detect a significant influence of SVO—in this case, the SVO of the dictator subject—on experimental behavior. This lends support to our hypothesis 6. Second, the dictator’s own contribution increases in the previous period’s dictator contribution. 4. Discussion and Conclusion The experimental literature on mechanisms fostering cooperation in dilemmas has lately predominantly focused on the effectiveness of punishment and reward. Recent work by Hamman et al. [20] and Bolle and Vogel [21] has extended this field to encompass inequalities in the power over one’s own and others’ decisions. Such asymmetries in the decision-making powers of economic actors are a frequent and important phenomenon outside the laboratory and, as such, merit careful analysis. Table 5. Overview of hypotheses and results. The table shows all hypotheses derived in Section 1and the corresponding results from Section 3. No. Statement Result 1a In the CCG, coordinators always contribute the full endowment. Rejected; only in 85% of cases 1b All subjects in the coordinator treatment select into the CCG. Rejected; median group size significantly smaller than 12 2a In the DCG, dictators always contribute nothing themselves and the full endowment for others. Rejected; only in 26% of cases 2b All subjects in the dictator treatment select into the DCG. Rejected; median group size significantly smaller than 12 3Subjects are more likely to choose the CCG than they are to choose the DCG. Supported; see Model 3 in Table 3 4Subjects’ likelihood of selecting into the DCG increases in the previous period’s dictator contribution. Not supported; see Model 4 in Table 3 5Subjects’ likelihood of selecting into the DCG increases in the previous period’s DCG size. Supported; see Models 2 and 4 in Tables 2and 3, respectively 6Pro-social dictators set their own contribution higher than pro-self dictators. Supported; see Model 5 in Table 4 7Subjects’ likelihood of selecting into the VCG increases in the previous period’s average VCG contribution. Supported; see Models 3 and 4 in Table 3 8Subjects’ likelihood of selecting into the ACG increases in the previous period’s average ACG contribution. Supported; see Models 1 and 2 in Table 2and Models 3 and 4 in Table 3 Hamman et al. [20] and Bolle and Vogel [21] demonstrate the possible efficiency gains from centralized decision-making in the provision of a public good. We extend their research by analyzing allocator mechanisms with different action spaces. We also implement direct competition between Games 2013,4604 different contribution mechanisms by allowing for endogenous group choice and investigate to what extent social preferences drive contribution and group choice behavior. We find that the vast majority of our subjects is willing to cede decision authority to a central planner in order to reap efficiency gains from improved coordination.19 We consider this result of great importance, since it clearly shows that human subjects are willing to submit to a randomly selected centralized authority if it leads to higher (expected) average payoffs. This is true both in a setting enforcing equality in payoffs and in one where the subject endowed with decision authority for the entire group can exploit this power to maximize her own payoffs at the expense of her team members’. Nonetheless, subjects are more likely to select into the allocator group in the first than in the second setting, and we investigate the factors driving this decision. Our data shows that subjects condition their group choice on historical group sizes and contribution behavior. Finally, we find that an allocator’s social value orientation plays a role in her contribution choice in the setting where she has the option to exploit her fellow group members. We summarize our findings in Table 5. Overall, they show that the allocator mechanism is not only more successful in establishing high contributions than a voluntary contribution scheme, but also wins out in a direct competition. We believe that these encouraging results merit further research into allocator contribution mechanisms for the provision of public goods and the accompanying power asymmetries. Acknowledgments We thank two anonymous referees and the audiences at the International Meeting of the Economic Science Association 2012, the Annual Meeting of the Austrian Economic Society 2013, the 15th International Conference on Social Dilemmas, the annual conference of the GfeW 2012, the Quantitative Sociology Colloquium at the ETH Z¨ urich and the research seminars at the Vienna Center of Experimental Economics and at the Faculty of Social and Economic Sciences at the University of Graz for valuable comments. All errors remain our own. Conflicts of Interest The authors declare no conflict of interest. Appendix Proof of the Dilution Effect in the Dictator Treatment Remember that Equation (4) posited the following expected payoff in the DCG: E[πi,DCG] = 1 nDCG ·E+λ nDCG ·E·(nDCG −1) Proof. 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