Fleiß, Jü gen; Palan, S e an
A icle
O coo dina o s and dic a o s: A public goods expe imen
Games
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Sugges ed Ci a ion: Fleiß, Jü gen; Palan, S e an (2013) : O coo dina o s and dic a o s: A public goods
expe imen , Games, ISSN 2073-4336, MDPI, Basel, Vol. 4, Iss. 4, pp. 584-607,
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A icle
O Coo dina o s and Dic a o s: A Public Goods Expe imen
J¨
u gen Fleiß 1and S e an Palan 2,3,*
1Ins i u e o S a is ics and Ope a ions Resea ch, Uni e si y o G az, Uni e si ¨
a ss asse 15, 8010 G az,
Aus ia; E-Mail: jue [email p o ec ed]
2Depa men o Banking and Finance, Uni e si y o Innsb uck, Uni e si ¨
a ss asse 15, 6020
Innsb uck, Aus ia
3Ins i u e o Banking and Finance, Uni e si y o G az, Uni e si ¨
a ss asse 15/F2, 8010 G az, Aus ia
*Au ho o whom co espondence should be add essed; E-Mail: [email p o ec ed];
Tel.: +43-512-507-7564; Fax: +43-512-507-2846.
Recei ed: 17 July 2013; in e ised o m: 11 Sep embe 2013 / Accep ed: 8 Oc obe 2013 /
Published: 10 Oc obe 2013
Abs ac : We expe imen ally in es iga e whe he human subjec s a e willing o gi e up
indi idual eedom in e u n o he bene i s o imp o ed coo dina ion. We conduc a
modi ied i e a ed public goods game in which subjec s in each pe iod i s decide which
o wo g oups o join. One g oup employs a olun a y con ibu ion mechanism, he o he
g oup an alloca o con ibu ion mechanism. The se up o he alloca o mechanism di e s
be ween wo ea men s. In he coo dina o ea men , he andomly selec ed alloca o can
se a uni o m con ibu ion o all g oup membe s, including he sel . In he dic a o ea men ,
he alloca o can choose di e en con ibu ions o he sel and all o he g oup membe s. We
ind ha subjec s willingly submi o au ho i y in bo h ea men s, e en when compe ing wi h
a olun a y con ibu ion mechanism. The alloca o g oups achie e high con ibu ion le els
in bo h ea men s.
Keywo ds: alloca o ; public goods game; sel -selec ion, ins i u ion choice, powe
In 2005, a special issue o Science lis ed he 25 a eas whe e scien is s pe cei ed he mos impo an
gaps in ou knowledge o da e [1]. These included he ques ion, aised by Pennisi [2], o how coope a i e
beha io e ol ed o o m he basis o he complex socie al s uc u es we obse e oday. She poin ed
ou he impo ance o in es iga ing which condi ions and ins i u ional se ings p omo e coope a ion in
si ua ions whe e indi iduals ha e an incen i e no o coope a e. A amous example o such a dilemma is
Games 2013,4585
o cou se he con ibu ion o a public good. In he s anda d se ing, indi iduals ha e s ong incen i es o
maximize hei own payo s by ee iding and no con ibu ing o he public good. As a esul , a g oup
o a ional ac o s would be unable o supply a public good.
A la ge numbe o labo a o y expe imen s ha e in es iga ed coope a ion in he public goods game
( o e iews, see [3,4]). In he mos common e sion o he epea edly played public goods game, each
indi idual in a g oup makes his o he own decision abou how much o he endowmen o con ibu e o a
public good in e e y pe iod. The esul s show ha con ibu ions end o s a ou a an a e age o a ound
50% and decline owa ds ze o [4,5]. Looking a indi idual beha io , a numbe o subjec s a e usually
ound o con ibu e in he i s ew pe iods o epea ed public goods games. O e ime, hei con ibu ions
decline as hey obse e o he subjec s ee iding and con ibu ing no hing. In he end, because o hese
condi ional coope a o s’ eac ions o he ee ide s, he public good no longe ge s p oduced [6–8].
These somewha disappoin ing indings on human coope a i e beha io in such dilemmas ha e been
quali ied by mo e ecen esul s. The e a e mechanisms ha can os e con ibu ions o he public
good. One such solu ion is mone a y punishmen , as in oduced by Os om, Ga dne and Walke [9].
Thei pape , and a numbe o ollow-up s udies, show ha (cen alized and decen alized) punishmen
and ewa d can s abilize con ibu ions a high le els [10–13].1Besides punishmen , o ing on he
implemen a ion o di e en p oposed con ibu ion ules has been shown o ha e a posi i e e ec [14,15].
We claim ha besides he ins umen s o punishmen and ewa d, di ec powe o e he decisions o
o he s can play an impo an ole when i comes o he success o collec i e ac ion in dilemma si ua ions.
Webe [16] de ines powe as “ he likelihood ha one pe son in a social ela ionship will be able,
e en despi e esis ance, o ca y ou his own will.” S uc u es o (asymme ic) powe dis ibu ions a e
omnip esen in e e yday li e and cha ac e ize whole socie ies, bu also g oups, (business) o ganiza ions
and he like [16,17]. Ye , despi e i s ob ious impo ance in e e yday li e, he discipline o economics
has no de o ed much ime o s udying powe o e he decisions o o he s ( o an analogous a gumen
and ano he ecen expe imen al s udy ega ding powe , see [18]).
K oll e al. [19] show ha con ibu ions o a public good inc ease i g oup membe s in a public
goods game can o e o a binding p oposal as opposed o making olun a y con ibu ions. One
pa icula ly no ewo hy ecen excep ion builds on he idea o binding subjec s o speci ic ac ions. I
employs a new con ibu ion mechanism in public good games, based on an asymme ic dis ibu ion o
powe : he alloca o mechanism. The wo s udies in oducing his opic a e Hamman e al. [20] and
Bolle and Vogel [21]. Bo h show ha , unde ce ain condi ions, one way o p omo ing he p o ision
o a public good is o es ablish an alloca o who has absolu e powe o e he decisions o all g oup
membe s. In he unique a ional expec a ions equilib ium, his alloca o is hen able o o ce all g oup
membe s o con ibu e hei ull endowmen o he public good, he eby maximizing he collec i e
ou come. Hamman e al. [20] and Bolle and Vogel [21] la gely con i m his heo e ical p edic ion
and show expe imen ally ha he use o an alloca o esul s in compa a i ely e y high con ibu ions o
he public good.
Whe e he wo s udies di e is in he speci ics o g oup membe s’ and alloca o s’ choice se s and in he
s uc u e o he expe imen . Hamman e al. [20] le g oup membe s elec an alloca o and ind ha g oups
1Fo a ecen e iew, see [4].
Games 2013,4586
ensu e ull p o ision o he public good p ima ily by elec ing p o-social alloca o s. Since each g oup o
nine holds a new elec ion e e y pe iod, hei se ing allows o punishmen by emo ing unde pe o ming
alloca o s om powe . Alloca o s who con ibu e ully o e e yone a e ound o be e-elec ed in almos
all cases. Bolle and Vogel [21] choose a di e en i s phase o hei expe imen . They ini ially le
subjec s play 10 pe iods o a public goods game wi h olun a y con ibu ions. This is ollowed by one
pe iod, whe e an alloca o is chosen (ei he andomly o by elec ion) o make he alloca ion decision o
he wo o he membe s o he h ee-pe son g oup. This sequence o olun a y (10 pe iods) and alloca o
con ibu ion phases (one pe iod) is epea ed wice, such ha subjec s play h ee alloca o pe iods in o al.
Like Hamman e al. [20], Bolle and Vogel [21] obse e highe con ibu ions in he alloca o se ing han
in he se ing wi h olun a y con ibu ions. In e es ingly, hey ind no s a is ically signi ican di e ences
be ween he elec ion and he andom selec ion ea men s.
The g ea success o he alloca o mechanism documen ed in hese wo s udies me i s u he esea ch.
We explo e i s pe o mance cha ac e is ics by (i) sys ema ically a ying he ac ion space o he alloca o
and by (ii) s udying whe he subjec s p e e g oups go e ned by he alloca o mechanism o e g oups
whe e hey can eely choose hei own con ibu ion when g oup choice is endogenous. No e ha he wo
p ecu so s udies implemen he alloca o mechanism in a way ha ei he o ces all subjec s o pa icipa e
o allows endogenous pa icipa ion, such ha non-pa icipa ing subjec s p o i om he public good o
pa icipa ing subjec s. In his second case, Hamman e al. [20] ind ha he alloca o mechanism is
no able o inc ease con ibu ions due o ee iding. Only when communica ion is possible do hal o
hei g oups choose o ans e hei decision igh s and achie e high con ibu ion le els. We build on
hese esul s and in es iga e whe he he ans o ma ion o he public good in o a club good, om which
only g oup membe s can p o i , is also able o os e he alloca o mechanism’s e iciency. Ou second
ques ion he e o e is o special impo ance, since i cap u es a subjec ’s willingness o submi o au ho i y
o he own bene i and he bene i o he whole g oup. This ques ion is also closely ela ed o a majo
inding in he discipline o new ins i u ional economics [22]. I s a es ha he olun a y pa icipa ion o
subjec s in inding a solu ion o coo dina ion p oblems subs an ially inc eases he likelihood o success.
Such endogenous ins i u ion choice has p e iously also been examined o he punishmen and ewa d
mechanisms men ioned abo e. One app oach is o le subjec s o e whe he hey wan o implemen , e.g.,
punishmen in he public goods game hey will la e be playing [23]. Ano he is o le subjec s sel -selec
in o g oups wi h di e en , exogenously ixed ins i u ional se ings. G¨
u e k e al. [24] ind ha subjec s
a e mo e likely o sel -selec in o g oups wi h sanc ioning ins i u ions han in o al e na i e g oups and
ha he likelihood o choosing he g oup wi h sanc ioning ins i u ion inc eases o e ime. In his way,
hey show ha when wo g oups wi h di e en ins i u ional se ings compe e agains each o he , he g oup
wi h a sanc ioning ins i u ion—due o he highe payo s i gene a es o i s membe s—p e ails in he
end. Hamman e al. [20] also p esen some o hese aspec s in hei expe imen s. They allow subjec s o
choose whe he hey wan o be pa o elec ing an alloca o who will hen make he con ibu ion decision
on hei behal o whe he hey wan o choose hei le el o con ibu ion hemsel es. The impo an
di e ence o he design o G¨
u e k e al. [24] (and his s udy) is ha subjec s who choose no o be
pa o he elec o al delega ion mechanism in Hamman e al. [20] none heless p o i om he public
goods con ibu ions made by subjec s who ha e delega ed hei decision powe . This allows subjec s
Games 2013,4587
who ha e no joined he delega ion mechanism o ee ide on i s ou comes.2Wi hou communica ion,
Hamman e al. [20] ob ain an a e age con ibu ion le el o only 11%. In his se ing, he alloca o
mechanism hus ails o sus ain high public goods con ibu ions. Whe he g oups go e ned by he
alloca o mechanism ha e an ad an age o e g oups wi h olun a y con ibu ion when one g oup does
no p o i om he con ibu ions o he o he is an impo an and unanswe ed ques ion.
Building on Hamman e al. [20] and Bolle and Vogel [21], we hus iden i y wo impo an
ques ions. Fi s , do subjec s p e e a g oup go e ned by he alloca o mechanism o e a g oup wi h
a olun a y con ibu ion mechanism? Second, which ac o s in luence subjec s’ g oup choice? The
p esen a icle answe s bo h o hese ques ions. As an addi ional inno a ion, we d ill down in o he
ole played by he alloca o ’s ac ion space. Speci ically, we compa e a ea men wi h wha we e m a
coo dina o —an alloca o who can choose one uni o m con ibu ion le el o all membe s o he g oup,
including he sel — o a ea men wi h a dic a o —an alloca o who can choose a con ibu ion le el o
he sel and a di e en , uni o m con ibu ion le el o all o he g oup membe s. This mimics many
se ings ou side he lab whe e a g oup leade o go e nmen es ablishes policies ha apply o all g oup
membe s equally (e.g., egula ions ha equi e e e y able-bodied male adul o con ibu e o he public
good o na ional de ense by ha ing o se e a e m in he mili a y, as exis s in many coun ies). Conside
as a loosely- ela ed example o ou se ing a coun y’s decision o join he Eu opean Union. This coun y
aces a adeo be ween gi ing up he eedom o decide on i s laws and egula ions en i ely on i s own
and abdica ing some o i s egula o y au ho i y o he EU ins i u ions in e u n o he bene i s om
g ea e coope a ion. This example sha es wi h ou design he ea u e ha leade ship o he g oup, in
his case, he p esidency o he council o he EU, o a es h ough all membe s a es, wi h each coun y
se ing only one e m. (Ano he example would be he decision by a s one-age human o join a ibe,
hus gi ing up indi idual eedom in o de o gain he abili y o join ly hun la ge game, which is a gued
o ha e con ibu ed o he ise o mode n ci iliza ion; see, e.g., [26]).
The emainde o his pape is s uc u ed as ollows. In Sec ion 1, we s a e ou esea ch ques ions and
de i e ou hypo heses. Sec ion 2ou lines he expe imen al design and p ocedu es. Resul s a e p esen ed
in Sec ion 3and discussed in Sec ion 4.
1. Resea ch Ques ion and Hypo heses
We in es iga e he ques ion o how socie al coo dina ion can a ise endogenously in esponse o
economic coo dina ion p oblems. We ake a s anda d public good game as ou wo kho se model and
augmen i by gi ing subjec s he eedom o selec in o one o wo g oups a he beginning o e e y
pe iod. In he olun a y con ibu ion g oup (VCG), hey play a s anda d public good game by deciding
how much o hei endowmen o keep o hemsel es and how much o in es in o a public good. I
subjec s selec in o he alloca o con ibu ion g oup (ACG), one g oup membe is andomly chosen o
se he con ibu ion le el o all ACG membe s.
2Kos eld e al. [25] showed ha cen alized punishmen ins i u ions a e able o p e ail in a se ing whe e non-pa icipa ing
playe s can ee ide on he con ibu ions o he playe s pa icipa ing in he cen alized punishmen ins i u ion. This leads
o high le els o e iciency in hei public goods expe imen s.

Games 2013,4588
Gi en a con ibu ion le el, we use he same payo unc ion in bo h g oups. Speci ically, a subjec ’s
payo o any one pe iod in ou expe imen is calcula ed as ollows:3
πi=Ei−ci+λ
nθ
·
nθ
X
j=1
cθ
j(1)
whe e πiis he payo o subjec i,Ei=E= 20 is a subjec ’s endowmen in each pe iod in expe imen al
cu ency uni s (ECU), ciis he subjec ’s con ibu ion o he public good in his pe iod, λ= 1.6is a
cons an de e mining he ma ginal pe capi a e u n (MPCR), nθis he numbe o subjec s in g oup
θ∈ {V CG, ACG}and Pnθ
j=1 cθ
jis he sum o all con ibu ions o subjec s jin g oup θin his pe iod.
The e u n om he public good is ende ed independen o he g oup size h ough he inclusion o nθin
he denomina o o he MPCR. I hus depends only on he a e age con ibu ion in he g oup ( his ollows
he design o Rockenbach and Milinski [27]). In he special case ha only a single subjec selec s in o
one o he g oups, he subjec ’s con ibu ion is au oma ically se o ze o, and no public good is gene a ed
(subjec s a e so in o med in he ins uc ions). No e ha subjec s ecei e in o ma ion abou hei g oup’s
size be o e making hei con ibu ion decision.
Figu e 1. T ea men design and e minology.
Coo dina o
Con ibu ion G oup
CCG
Alloca o Con ibu ion
G oup
ACG
Volun a y Con ibu ion
G oup
VCG
Dic a o Con ibu ion
G oup
DCG
Coo dina o T ea men :
The alloca o can se a uni o m
con ibu ion le el o all g oup
membe s.
The alloca o (= andomly
selec ed g oup membe )
decides on con ibu ions o all
g oup membe s. T ea men s
di e in he alloca o ac ion
space.
Dic a o T ea men : The
alloca o can se a di e en
con ibu ion le el o
himsel /he sel .
Hamman e al. [20] and Bolle and Vogel [21] implemen ed he alloca o decision in a way ha allowed
he alloca o o se a di e en con ibu ion o he sel han o he o he g oup membe s. This allows
o he ise o “co up ion”, which is how we e e o he case whe e he alloca o does no con ibu e
o he public good.4Ou design expands on his idea by modeling wo di e en ypes o alloca o
decision op ions. We will con inue o use “alloca o ” and ACG as he gene al e ms, bu will dis inguish
be ween a “coo dina o ” and a “dic a o ” ea men in ou design. In he o me , he coo dina o can
choose a con ibu ion le el, which hen applies o all g oup membe s, including he sel . In he la e ,
he dic a o can choose wo con ibu ion le els, one o which applies o all g oup membe s excluding
3We supp ess he pe iod index in o de o s eamline he no a ion.
4No e ha ou ins uc ions gene ally con ained neu al wo ding, o example, e e ing o he VCG (ACG) as he “g oup
wi h indi idual con ibu ion choice” (“g oup wi h con ibu ion choice by a andomly de e mined playe ”).
Games 2013,4589
he sel , while he o he applies only o he sel . In keeping wi h he ocabula y jus laid ou , we will be
speaking o wo o ms o ACGs— he coo dina o con ibu ion g oup (CCG) and he dic a o con ibu ion
g oup (DCG). Figu e 1illus a es his e minology. Finally, we wish o explo e he impac o subjec s’
social p e e ences on hei beha io in ou expe imen . Fo his eason, we elici hei social alue
o ien a ion using he social alue o ien a ion (SVO) slide measu e de eloped by Mu phy e al. [28].
1.1. Ra ional Expec a ions P edic ions
To p edic he g oup choice, we ha e o ake a look a he expec ed con ibu ions and payo s in each o
he wo g oups. In he VCG, he a ionally5expec ed beha io is no o con ibu e, yielding an expec ed
payo o e e y subjec equal o he endowmen . (This is also he minimax payo in he VCG.) In he
ACGs, he e a e di e en p edic ions o ou wo ea men s. Gi en ha he coo dina o can only se one
uni o m con ibu ion le el o all g oup membe s, i is immedia ely appa en ha o any λ > 1(and
assuming E > 0), he p o i -maximizing s a egy is o se he con ibu ion le el equal o he common
endowmen , E. The payo o bo h he coo dina o and he o he g oup membe s, hen, is he payo
om ull coope a ion:
πi,CCG =λ
nCCG
·E·nCCG (2)
Gi en ha λ= 1.6and E= 20 in ou se ing, we hus de i e he i s pa o ou i s hypo hesis:
Hypo hesis 1a. In he CCG, coo dina o s always con ibu e he ull endowmen .
In he coo dina o ea men , he expec ed payo as a membe o he alloca o g oup is highe 6 han he
minimax payo in he olun a y con ibu ion g oup, which equals he endowmen E.7Unde a ional
expec a ions, we would he e o e expec all subjec s o choose he alloca o g oup in he coo dina o
ea men despi e hei lack o knowledge, a he ime o making he decision, o he subsequen ly
esul ing g oup size. We use his benchma k o he de i a ion o he second pa o ou i s hypo hesis:
Hypo hesis 1b. All subjec s in he coo dina o ea men selec in o he CCG.
In he dic a o ea men , we asse ha a a ional alloca o would se he con ibu ion o all g oup
membe s equal o hei endowmen s and se a con ibu ion o ze o o he sel . This yields he ollowing
payo s:
πi,DCG =


E+λ
nDCG ·E·(nDCG −1) i subjec iis he dic a o , and
λ
nDCG ·E·(nDCG −1) i subjec iis no he dic a o
(3)
We e lec he incen i es induced by his payo unc ion in he i s pa o ou second hypo hesis.
5No e ha a ional in his case includes he assump ion ha he ac o s a e only in e es ed in maximizing hei own payo
wi hou ega d o he payo o o he s.
6S ic ly speaking, his is only ue i subjec s assign a posi i e p obabili y o nCCG >1.
7This esul holds o any λ > 1and, hus, o any public good.
Games 2013,4590
Hypo hesis 2a. In he DCG, dic a o s always con ibu e no hing hemsel es and he ull endowmen o
all o he g oup membe s.
Since e e y playe who joins he DCG has a chance o 1nDCG o become he dic a o , he
condi ionally expec ed payo (assuming ull con ibu ion) o joining he DCG, gi en a g oup size o
nDCG, would be:
E[πi,DCG] = 1
nDCG
·E+λ
nDCG
·E·(nDCG −1)(4)
whe e Eis he condi ional expec a ions ope a o assuming equilib ium play (i.e., ull con ibu ion
in he ACG; no con ibu ion in he VCG). I ollows om Equa ions (2) and (4), as well as
om ou ea men o he special case o a g oup size o one ha E[πi,DCG]≥E[πi,V CG],wi h
E[πi,DCG] = E[πi,V CG]i nDCG = 1. Thus, e en hough he esul ing g oup sizes a e as ye
unde e mined when subjec s make hei g oup choice, selec ing in o he VCG is none heless a dominan
s a egy. This is also he case o he wo s possible ou come in he DCG when only wo subjec s join
he DCG.8This leads o he second pa o ou second hypo hesis:
Hypo hesis 2b. All subjec s in he dic a o ea men selec in o he DCG.
Despi e hei heo e ical alidi y, we judge i likely ha hypo heses 1a and 1b, as well as
hypo heses 2a and 2b will no hold in ou expe imen s. Expe imen al economis s (among o he s) ha e
shown ha people do no beha e in an exclusi ely payo maximizing manne . In ou se ing, possible
easons o o -equilib ium beha io include he he e ogenei y o social p e e ences, bounded a ionali y,
salience e ec s, a e sion o isk and/o losses and a dislike o compe ing pe se. Un o una ely, he e
is a la ge numbe o di e en heo ies o , e.g., social p e e ences, such ha i is no possible o include
all o hem wi h p ecise p edic ions. We will he e o e o mula e some hypo heses ega ding expec ed
de ia ions om pe ec ly a ional beha io based on social alue o ien a ion and inequali y a e sion.
1.2. Social P e e ence P edic ions
Social p e e ence models (and also social alue o ien a ion) assume ha indi iduals a e no conce ned
abou hei own payo alone, bu also abou he payo s o o he s and he ela i e sizes o hei own and
o he s’ payo s. One speci ic o m o social p e e ences is inequali y-a e sion. Ou come based models
o inequali y a e sion assume ha subjec s a e a e se o di e ences in ou comes (see, e.g., [29,30]). This
allows us o make a p edic ion ega ding he di e ences in g oup choice be ween he coo dina o and
dic a o ea men s. Since no inequali y is possible in he CCG, inequali y a e sion canno be a cause o
subjec s choosing he VCG in he coo dina o ea men . This is di e en in ou dic a o ea men . He e,
he dic a o can choose di e en con ibu ion le els o himsel and o he o he DCG membe s, he eby
inc easing his payo ela i e o he o he g oup membe s’. This educes he u ili y o inequali y-a e se
8Following om Equa ion (4), his asse ion implies he ollowing inequali y: 1nACG ·E+λnACG ·E·(nACG −1) > E.
I is easy o show ha i simpli ies o λ > 1i E > 0and n > 1.
Games 2013,4591
subjec s and ende s he VCG ela i ely mo e a ac i e o hem.9Since we assume ha he e likely a e
such subjec s in ou subjec pool, we e lec his in ou nex hypo hesis:
Hypo hesis 3. Subjec s a e mo e likely o choose he ACG in he coo dina o ea men han in he
dic a o ea men .
Once we d op he assump ion o a ional expec a ions, subjec s can be assumed o upda e hei
expec a ions o o he pa icipan s’ beha io based on hei obse a ions o pas ou comes. We expec
an e ec o he amoun o he dic a o con ibu ion in he p e ious pe iod on subjec s’ g oup choice in
he subsequen pe iod.
Hypo hesis 4. Subjec s’ likelihood o selec ing in o he DCG inc eases in he p e ious pe iod’s
dic a o con ibu ion.
As Equa ion (3) makes clea , he nega i e e ec s o low dic a o con ibu ions in he DCG a e dilu ed
wi h inc easing g oup size, since he cos o dic a o ee iding is join ly bo ne by mo e g oup membe s.
We expec ha his dilu ion e ec will make i mo e likely o dic a o ea men subjec s o join he DCG
when hey expec many o he s o do so.10 No e, howe e , ha ou subjec s do no know he g oup size
o he pe iod o which hey a e cu en ly making hei g oup choice. We conjec u e ha hey will use
he g oup size in o ma ion om he p e ious pe iod as a p oxy o he cu en pe iod’s DCG size when
o ming hei expec a ions o he la e .11
Hypo hesis 5. Subjec s’ likelihood o selec ing in o he DCG inc eases in he p e ious pe iod’s
DCG size.
We also explo e he impac o alloca o s’ social alue o ien a ion on hei decisions in he expe imen .
Subjec s wi h a p o-social alue o ien a ion no only ca e abou hemsel es, bu also abou ele an
o he s (see, e.g., [31,32]). On he o he hand, p o-sel indi iduals a e mo e in e es ed in hei own
payo . P e ious expe imen s show ha a p o-social alue o ien a ion co ela es wi h coope a i e
beha io in economic expe imen s (see, e.g., [33]).12 On his basis, we expec p o-social dic a o s
o se a highe con ibu ion le el o hemsel es han do p o-sel dic a o s. In he CCG, p o-social
and p o-sel coo dina o s should beha e he same way (se ing he con ibu ion o e e yone equal o
he endowmen ).
Hypo hesis 6. P o-social dic a o s se hei own con ibu ion highe han p o-sel dic a o s.
9No e ha dic a o s wi h social p e e ences (like inequali y-a e sion o de i ing posi i e u ili y om he payo s o o he s)
migh hemsel es con ibu e ( ully) o he public good (see hypo hesis 6). We hank an anonymous e e ee o poin ing
his ou .
10 No e ha he dilu ion e ec is coun e ac ed by he dec ease in p obabili y o being assigned he dic a o ole wi h he
a endan highe possible payo . Re e o he Appendix in Sec ion 4 o a p oo ha he i s e ec ou weighs he second.
S ic ly speaking, ou a gumen is based on he ne e ec .
11 While we do conside his ques ion o be in e es ing, we did no judge i impo an enough o explici ly elici g oup size
expec a ions, which ca ies a isk o causing an expe imen e demand e ec .
12 Fo a e iew, see [34].
Games 2013,4598
Figu e 4. O e all end in a e age g oup size o e ime in he wo ea men s. The igu e
displays he a e age g oup size in each o he en pe iods sepa a ely o he dic a o and he
coo dina o ea men s. The da a o ounds 1 and 2 a e pooled. The dashed lines a e linea
p edic ions. The hin lines a e a e age g oup sizes in indi idual 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
Coo dina o Dic a o
ACG G oup Size VCG G oup Size
G oup Size
Pe iod
Nex , we conduc a eg ession analysis o he agg ega e da a, which is p esen ed in Table 2. In he
models (which we i indi idually o each ea men ), we con ol o he ound, he pe iod and he
in e ac ion be ween he wo, allowing he slope o he pe iods o a y be ween ounds. We also include
p e ious pe iod da a on he a e age size o , and he a e age con ibu ion in, he ACG.

Games 2013,4599
Table 2. G oup size. The able shows he esul s o OLS eg essions o he CCG and
DCG g oup sizes on a numbe o eg esso s. Round is 1 (2) in he i s (second) o he
wo 10-pe iod sequences. Pe iod2 equals he pe iod numbe Pe iod in ound 2 and ze o
o he wise. The emaining a iables a e he lagged a e age con ibu ions in he ACG and he
lagged ACG g oup size (o he DCG in he eg ession o he dic a o ea men , o he CCG
in he analysis o he coo dina o ea men ) and he lagged con ibu ion o he dic a o in he
DCG.
Model 1 Model 2
Reg esso s CCG G oup Size DCG G oup Size
Round 0.098 (0.538) 0.690 (0.516)
Pe iod 0.069 (0.071) 0.060 (0.056)
Pe iod2 0.041 (0.104) −0.078 (0.069)
Lagged A e age Con ibu ion in ACG 0.103 (0.016) *** 0.089 (0.034) **
Lagged Dic a o Con ibu ion in DCG 0.033 (0.014) *
Lagged G oup Size in ACG 0.287 (0.157) 0.393 (0.059) ***
Cons an 4.537 (0.937) ** 2.942 (0.889) **
R20.30 0.37
Adjus ed R20.25 0.34
N 72 117
*p<0.1; ** p<0.05; *** p<0.01. S anda d e o s clus e ed a he session le el (in pa en heses).
Ou esul s show ha he ime e ec isible in Figu e 4is no signi ican in ei he ea men
when con olling o he a iables ha we e iden i ied as ele an in ou hypo heses in Sec ion 1.
Models 1 and 2 sha e one s a is ically signi ican e ec : a la ge a e age ACG con ibu ion in he
p e ious ound esul s in a la ge cu en ACG g oup size, suppo ing ou hypo hesis 8. I also implies
ha when he alloca o con ibu es ela i ely li le, he g oup size o he VCG inc eases in he ollowing
pe iod. Fu he mo e, o he dic a o ea men only, we ind a signi ican e ec o he DCG g oup size
in he p e ious pe iod. This p o ides suppo o he p esence o he dilu ion e ec , as conjec u ed in
hypo hesis 5. Finally, we ind a signi ican e ec o he dic a o con ibu ion in he p e ious pe iod on
he DCG g oup size (hypo hesis 4).16
We con inue ou analysis by in es iga ing indi idual subjec s’ g oup choice beha io using P obi
models.17 Table 3p esen s he wo eg ession models we belie e bes e lec he s uc u al ela ionships
in ou da a. In Model 3, we include he Round and Pe iod a iables, a ea men dummy and a
a iable con aining ou subjec s’ social alue o ien a ion as measu ed using he ins umen de ined in
Mu phy e al. [28]. Highe alues o he SVO measu e indica e a g ea e willingness o gi e up own
16 Tobi eg ession censo ed a ze o and 12 yields simila esul s.
17 Robus ness checks con i m ha ou main esul s a e s able wi h ega d o he use o a logi model and o he inclusion
o exclusion o di e en ques ionnai e i ems. A ansla ion o he ques ions is p o ided in he Elec onic Supplemen a y
In o ma ion.
Games 2013,4600
income o bene i o he s. We also include an in e ac ion o SVO wi h he ea men dummy, as well as
a iables con aining in o ma ion on he p e ious pe iod’s a e age con ibu ions in he VCG and ACG
(A gCon ibVCG L and A gCon ibACG L) and on he size o he ACG (and, sepa a ely, o he DCG)
in he p e ious pe iod (G oupSizeACG L and G oupSizeACG L x Dic a o ).
Table 3. De e minan s o alloca o g oup choice. The able shows he esul s o P obi
eg essions o IsACG on a numbe o eg esso s. IsACG is a dummy equal o ze o (one) i
he subjec chooses he VCG (ACG) in a pe iod. Dic a o is a dummy a iable equal o ze o
(one) in he coo dina o (dic a o ) ea men . Round is 1 (2) in he i s (second) o he wo 10-
pe iod sequences. Pe iod2 equals he pe iod numbe Pe iod in ound 2 and ze o o he wise.
SVO is he social alue o ien a ion o he subjec s, measu ed using he slide -measu e om
Mu phy e al. (2011), and SVO x Dic a o is SVO in e ac ed wi h Dic a o . The emaining
a iables a e he lagged a e age con ibu ions in he ACG and VCG, he lagged ACG g oup
size (pooled and in he dic a o ea men only) and he lagged con ibu ion o he dic a o
in he dic a o ea men (no e ha he model ha includes his a iable solely uses dic a o
ea men da a). Logi es ima ion and logi panel eg ession yield simila esul s. Robus ness
checks, whe e we include a ious ques ionnai e esponse i ems and in e ac ion e ms, yield
no clea e ec s om he con ol a iables, bu lea e he main e ec s unchanged.
Reg esso s Model 3 Model 4
Subsample All cases Dic a o ea men
Dic a o −1.284 (0.679) *
Round −0.127 (0.187) −0.012 (0.303)
Pe iod 0.000 (0.017) 0.008 (0.026)
Pe iod2 0.026 (0.027) 0.010 (0.041)
SVO −0.010 (0.011)
SVO x Dic a o 0.020 (0.015) 0.010 (0.010)
A gCon ibACG L 0.030 (0.008) *** 0.024 (0.011) **
A gCon ibVCG L −0.046 (0.012) *** −0.038 (0.012) ***
G oupSizeACG L 0.044 (0.061)
G oupSizeACG L x Dic a o 0.085 (0.066) 0.119 (0.038) ***
Dic Con ib L 0.009 (0.007)
Cons an 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. S anda d e o s clus e ed a he subjec le el (in pa en heses).
As p edic ed in hypo hesis 3, we ind a nega i e ea men e ec . Subjec s a e less likely o join he
ACG in he dic a o ea men . Ou model also shows ha he likelihood o a subjec selec ing in o he
ACG as opposed o he VCG inc eases in he a e age con ibu ion in he ACG in he p e ious pe iod,
hus lending u he suppo o ou hypo hesis 8. Con e sely, highe con ibu ions in he VCG in he
Games 2013,4601
p e ious pe iod dec ease he likelihood o subjec s joining he ACG. This esul suppo s hypo hesis 7.
We also ind ha g ea e social alue o ien a ion o a subjec canno be shown o play a ole.18 Finally,
he esul s do no yield any e idence o subjec s being mo e likely o selec in o he ACG in la e pe iods
o in he second ound.
Model 4 di e s om Model 3 in ha i uses only he dic a o ea men da a and con ains he amoun
o he p e ious pe iod’s dic a o con ibu ion as an addi ional a iable. We ind a s a is ically signi ican
e ec o he lagged size o he DCG, bu no he ACG in gene al, lending u he suppo o he dilu ion
e ec o hypo hesis 5. Model 4 also shows a signi ican e ec o he lagged a e age con ibu ion in
he DCG, bu none o he lagged dic a o con ibu ion. Hypo hesis 4does no ecei e suppo om his
esul . The a e age con ibu ion in he VCG in he p e ious pe iod shows a highly signi ican nega i e
coe icien , again, in line wi h ou hypo hesis 7. Jus as in he pooled analysis, he e appea s no o be a
ma e ial e ec o SVO on g oup choice.
18 Two subjec s did no ill in he SVO ques ionnai e co ec ly and a e, he e o e, excluded om all analyses employing
social alue o ien a ion da a. Fu he mo e, he session 11 da a a e no included, since no SVO o o he ques ionnai e
i ems we e elici ed, due o he se e c ash.
Games 2013,4602
Table 4. De e minan s o dic a o con ibu ion choice. The able shows he esul s o an
OLS eg ession o he dic a o ’s own con ibu ion on a numbe o eg esso s. Round is 1
(2) in he i s (second) o he wo 10-pe iod sequences. Pe iod2 equals he pe iod numbe
Pe iod in ound 2 and ze o o he wise. SVO is he social alue o ien a ion o he dic a o ,
measu ed using he slide -measu e om Mu phy e al. [28]. The emaining a iables a e
he lagged a e age con ibu ion in he DCG, he concu en DCG g oup size and he lagged
dic a o con ibu ion. The inclusion o he lagged a iables leads o he exclusion o he
obse a ions om pe iod 1 in ounds 1 and 2. Tobi eg ession censo ed a ze o and 20
yields simila esul s. Robus ness checks, whe e we include a ious ques ionnai e esponse
i ems and in e ac ion e ms, yield no clea e ec s om he con ol a iables, bu lea e he
main e ec s unchanged.
Reg esso s Model 5
Round −2.225 (4.214)
Pe iod −0.691 (0.454)
Pe iod2 0.417 (0.632)
A gCon ibDCG L −0.159 (0.266)
G oupSizeDCG 0.736 (0.486)
Dic a o Con ibu ion L 0.325 (0.104) ***
SVO 0.127 (0.060) **
Cons an 5.132 (7.438)
R20.23
Adj. R20.17
N 107
*p<0.1; ** p<0.05; *** p<0.01. S anda d e o s clus e ed a he subjec le el (in pa en heses).
Games 2013,4603
3.3. Con ibu ions
We nex ocus on dic a o s’ con ibu ion beha io in he DCG. Table 4con ains ou OLS eg ession
esul s o he dic a o ’s own con ibu ion (Model 5). We con ol o a ime end, he lagged
con ibu ions, he g oup size o he ACG, he lagged dic a o con ibu ion and SVO. Fi s , his is he
only ins ance whe e we de ec a signi ican in luence o SVO—in his case, he SVO o he dic a o
subjec —on expe imen al beha io . This lends suppo o ou hypo hesis 6. Second, he dic a o ’s own
con ibu ion inc eases in he p e ious pe iod’s dic a o con ibu ion.
4. Discussion and Conclusion
The expe imen al li e a u e on mechanisms os e ing coope a ion in dilemmas has la ely p edomi-
nan ly ocused on he e ec i eness o punishmen and ewa d. Recen wo k by Hamman e al. [20] and
Bolle and Vogel [21] has ex ended his ield o encompass inequali ies in he powe o e one’s own and
o he s’ decisions. Such asymme ies in he decision-making powe s o economic ac o s a e a equen
and impo an phenomenon ou side he labo a o y and, as such, me i ca e ul analysis.
Table 5. O e iew o hypo heses and esul s. The able shows all hypo heses de i ed in
Sec ion 1and he co esponding esul s om Sec ion 3.
No. S a emen Resul
1a In he CCG, coo dina o s always con ibu e he ull
endowmen .
Rejec ed; only in 85% o cases
1b All subjec s in he coo dina o ea men selec in o he
CCG.
Rejec ed; median g oup size signi ican ly smalle han
12
2a In he DCG, dic a o s always con ibu e no hing
hemsel es and he ull endowmen o o he s.
Rejec ed; only in 26% o cases
2b All subjec s in he dic a o ea men selec in o he
DCG.
Rejec ed; median g oup size signi ican ly smalle han
12
3Subjec s a e mo e likely o choose he CCG han hey
a e o choose he DCG.
Suppo ed; see Model 3 in Table 3
4Subjec s’ likelihood o selec ing in o he DCG inc eases
in he p e ious pe iod’s dic a o con ibu ion.
No suppo ed; see Model 4 in Table 3
5Subjec s’ likelihood o selec ing in o he DCG inc eases
in he p e ious pe iod’s DCG size.
Suppo ed; see Models 2 and 4 in Tables 2and 3,
espec i ely
6P o-social dic a o s se hei own con ibu ion highe
han p o-sel dic a o s.
Suppo ed; see Model 5 in Table 4
7Subjec s’ likelihood o selec ing in o he VCG inc eases
in he p e ious pe iod’s a e age VCG con ibu ion.
Suppo ed; see Models 3 and 4 in Table 3
8Subjec s’ likelihood o selec ing in o he ACG inc eases
in he p e ious pe iod’s a e age ACG con ibu ion.
Suppo ed; see Models 1 and 2 in Table 2and Models 3
and 4 in Table 3
Hamman e al. [20] and Bolle and Vogel [21] demons a e he possible e iciency gains om
cen alized decision-making in he p o ision o a public good. We ex end hei esea ch by analyzing
alloca o mechanisms wi h di e en ac ion spaces. We also implemen di ec compe i ion be ween

Games 2013,4604
di e en con ibu ion mechanisms by allowing o endogenous g oup choice and in es iga e o wha
ex en social p e e ences d i e con ibu ion and g oup choice beha io . We ind ha he as majo i y o
ou subjec s is willing o cede decision au ho i y o a cen al planne in o de o eap e iciency gains om
imp o ed coo dina ion.19 We conside his esul o g ea impo ance, since i clea ly shows ha human
subjec s a e willing o submi o a andomly selec ed cen alized au ho i y i i leads o highe (expec ed)
a e age payo s. This is ue bo h in a se ing en o cing equali y in payo s and in one whe e he subjec
endowed wi h decision au ho i y o he en i e g oup can exploi his powe o maximize he own payo s
a he expense o he eam membe s’. None heless, subjec s a e mo e likely o selec in o he alloca o
g oup in he i s han in he second se ing, and we in es iga e he ac o s d i ing his decision. Ou
da a shows ha subjec s condi ion hei g oup choice on his o ical g oup sizes and con ibu ion beha io .
Finally, we ind ha an alloca o ’s social alue o ien a ion plays a ole in he con ibu ion choice in he
se ing whe e she has he op ion o exploi he ellow g oup membe s.
We summa ize ou indings in Table 5. O e all, hey show ha he alloca o mechanism is no only
mo e success ul in es ablishing high con ibu ions han a olun a y con ibu ion scheme, bu also wins
ou in a di ec compe i ion. We belie e ha hese encou aging esul s me i u he esea ch in o alloca o
con ibu ion mechanisms o he p o ision o public goods and he accompanying powe asymme ies.
Acknowledgmen s
We hank wo anonymous e e ees and he audiences a he In e na ional Mee ing o he Economic
Science Associa ion 2012, he Annual Mee ing o he Aus ian Economic Socie y 2013, he 15 h
In e na ional Con e ence on Social Dilemmas, he annual con e ence o he G eW 2012, he Quan i a i e
Sociology Colloquium a he ETH Z¨
u ich and he esea ch semina s a he Vienna Cen e o Expe imen al
Economics and a he Facul y o Social and Economic Sciences a he Uni e si y o G az o aluable
commen s. All e o s emain ou own.
Con lic s o In e es
The au ho s decla e no con lic o in e es .
Appendix
P oo o he Dilu ion E ec in he Dic a o T ea men
Remembe ha Equa ion (4) posi ed he ollowing expec ed payo in he DCG:
E[πi,DCG] = 1
nDCG
·E+λ
nDCG
·E·(nDCG −1)
P oo . Fo he dilu ion e ec o ob ain, he ollowing inequali y mus hen hold ( o exposi ional
con enience, we supp ess he DCG subsc ip ):
19 No e ha he alloca o mechanism a he same ime dec eases he isk o exploi a ion and impac s payo inequali y.
Fu he esea ch is needed o disen angle he di e en ial e ec o hese ac o s.
Games 2013,4605
1
n·E+λ
n·E·(n−1)<1
n+c·E+λ
n+c·E·(n+c−1)(5)
whe e cis an a bi a y, posi i e in ege . Inequali y (5) can be simpli ied o:
c < λc (6)
Inequali y (6) is ul illed o any n∈N+,λ > 1and E > 0and, hus, o any public good. This also
ex ends o ou pa ame e iza ion, whe e λ= 1.6.
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