The Public Goods game revisited *

Transcription

1 The Publc Goods game revsted * Daan van Soest a*, Jan Stoop b, Jana Vyrastekova c a VU Unversty Amsterdam, Department of Spatal Economcs and IVM, Amsterdam, the Netherlands, and Tlburg Unversty, Department of Economcs and CentER, Tlburg, the Netherlands. b Erasmus Unversty Rotterdam, Department of Appled Economcs, Rotterdam, the Netherlands. c Njmegen Unversty, Department of Economcs, Njmegen, the Netherlands. Abstract Play n standard Publc Goods games suggests that on average, humans are qute wllng to cooperate n mult-person socal dlemmas. Yet cooperaton s largely absent n real world socal dlemmas where the benefts of cooperaton are hghest, such as n envronmental problems. We hypothesze that ths dscrepancy s due to the fact that n the Publc Goods game the worst free rders can do s to not contrbute to the common good, whle n most real world envronmental stuatons they can actually undo the good works of others. We construct a modfed verson of the standard Publc Goods game that allows for negatve contrbutons to the common good, and show that average behavor s not statstcally dfferent from the Nash equlbrum predcton n any of the perods the game lasts. JEL Classfcaton: C72, C92, D74. Key words: socal dlemma, publc goods game, laboratory experments. * We would lke to thank Davd Rand for hs valuable comments on the desgn and on an earler verson of the paper. Please send all comments to Daan van Soest, Department of Economcs, Tlburg Unversty, PO Box 90153, 5000 LE Tlburg, The Netherlands; d.p.vansoest@uvt.nl. 1 Introducton Standard game theory predcts a lack of cooperaton n socal dlemma stuatons. Yet economc experments present evdence to the contrary even f the expermental games are desgned to stack the de aganst cooperaton. The man workhorse of ths lterature s the fntely repeated Publc Goods game (also known as the Voluntary Contrbuton Mechansm, VCM), whch has been studed extensvely over the past 30 years. Each subject receves an

2 endowment that she can keep, or nvest n a group project that benefts all members of her group. Aggregate payoffs are maxmzed f all subjects nvest ther entre endowment n the group project, but the domnant strategy n ths game s to pocket one s endowment. Despte the standard game-theoretc predcton of zero contrbutons, subjects typcally nvest, on average, between 40 and 60% of ther endowment n the frst perod of the nteracton. Contrbutons declne over tme, but only become (approxmately) zero n the very last perod (Ledyard 1995, Chaudhur 2010) even f the game lasts as long as 50 perods (Gächter et al. 2008). These observatons (and results from other expermental games that measure prosocalty n behavor, such as the Dctator game, see Forsythe et al and Engle 2011) have nspred researchers to develop models ncorporatng other-regardng preferences such as altrusm (Andreon and Mller 2002), nequalty averson (Bolton and Ockenfels 1998, Fehr and Schmdt 1999), and preferences for condtonal cooperaton (Rabn 1993). We dspute nether the fact that humans are endowed wth other-regardng preferences nor that the amount of cooperaton n the canoncal VCM games s much greater than can be explaned by standard game theory. However, we queston the degree to whch behavor n the VCM game n ts canoncal form, nforms us about the propensty of humans to cooperate n real-world socal dlemmas. The mean reason for ths s that n the VCM game selfsh ndvduals have a domnant strategy to contrbute nothng to the common good, whle n many real-world nstances, ncludng (vrtually) all envronmental problems, selfsh ndvduals can actually undo some or all of the good works of others. Mtgatng clmate change has been labeled the greatest externalty good of all (cf. Stern 2007), but the clmate change game does not have a domnant strategy of zero abatement. The more some agents nvest n mprovng ther energy effcency or n utlzng renewable energy sources, the lower the prce of fossl fuels, and the more attractve t becomes for other agents to actually ncrease ther fossl fuel consumpton (and the global net effect may even be an actual ncrease n total emssons, gvng rse to the so-called Green Paradox ; cf. Snn 2008). And smlar leakage effects play a role n many other socal dlemmas traffc congeston s another example n pont. In ths paper, we present the results from a slghtly modfed verson of the standard Publc Good game, the Clam game. Ths Clam game s mean feature s that cooperatve actons of one agent can be undone by another. Subjects smultaneously choose how much to nvest n a publc fund, where contrbutons can be postve or negatve. Negatve contrbutons (or clams) ncrease the decson maker s payoffs at the expense of the sze of the publc good. If the total net contrbutons are stll postve, the publc fund pays a postve return to each member of the group; f the total net contrbutons are zero or negatve, the returns from the publc fund are zero. We compare the outcomes of a standard Publc Good game wth two dfferent specfcatons of the Clam game, one that yelds the same benefts of cooperaton as n the PG game, and one n whch the payoffs to defecton are the same as n the PG game. We fnd that n the Clam games group nvestments n the publc good are not sgnfcantly dfferent from zero not when averaged over all perods, and also not when just analyzng contrbutons n the frst perod. We thus fnd that standard game theory s a good predctor of aggregate play n the Clam game even n the early perods of each sesson. Moreover, we also observe that pro-socal ndvduals (as classfed on the bass of the postve contrbutons they make n the frst perod of the nteracton) very rapdly revert to Nash behavor much faster than n the standard VCM game. Whle we do not dspute that a large share of humans has other-regardng preferences (cf. Fschbacher et al. 2001), our results ndcate that these preferences may not always translate nto pro-socal behavor n the

3 real world. Indeed, our results echo the dscusson whether a model s worth should be evaluated on the bass of whether the assumptons are realstc, or whether ts predctve power s the key crteron for evaluaton. If a model s predctve power s most mportant (as argued by Mlton Fredman n hs 1954 paper), our results suggest that at least n some socal dlemma contexts, t s suffcent to use smple models based on homo economcus. A substantal share of manknd cares about more than just ther own prvate welfare, but n those contexts the strategc envronment s such that we can assume as f they are all selfsh, and stll predct ther behavor well. Wthn the VCM lterature, the papers by Khadjav and Lange (2011), McCarter et al. (2011), and Cox et al. (2013) are closest to ours. Khadjav and Lange (2011) analyze the mpact of framng on subjects contrbutons to the publc good. The three key treatments dffer n both the acton set (whether subjects can only gve, only take, or can both gve or take) and the ntal endowment n the publc account (empty, some share of the group s total budget, or all of the group s budget). Khadjav and Lange fnd that average contrbutons to the publc good are sgnfcantly smaller when subjects can only take (a takng game ) than when they can only gve (the VCM game); cf. Andreon (1995). But they fnd no sgnfcant dfferences between play n the standard VCM game and the game n whch they can gve or take (n the treatment n whch some -but not all- of the budget has already been allocated to the publc good). Our desgn complements that by Khadjav and Lange (2011) as takng does not just reduce one s own contrbutons to the publc good, but actually decreases those of others. In our experment, a subject contrbutng her entre endowment to the publc account may dscover that ultmately the publc account contans fewer ponts than she contrbuted f all other subjects decded to take rather than to gve. Whle the experment by Khadjav and Lange yelds valuable nsghts nto the preferences of humans and how the benchmarks of good and bad behavor depend on the avalable acton space (as n Lst 2007 and Bardsly 2008), our experments complement these nsghts by explorng the mpact of changng the strategc envronment. McCarter et al. (2011) explore the mpact of allowng subjects to gve or take n a threshold Publc Goods game, and fnd that the opton to take results show less cooperaton than n the standard setup, where takng s not an opton. Nevertheless, they stll report cooperaton levels that are stll far removed from the Nash equlbrum. The paper by Cox et al. (2013) s closest to ours. They conduct a sequental publc goods game n whch three group members smultaneously decde how much of ther tokens to contrbute to the publc account, whle the fourth can then ether contrbute donate to the publc good, or take from t (all, or none). They fnd that contrbutons are much smaller n ths treatment than n the standard publc goods game; our experment complements these nsghts by showng that the strategc effect can result n all subjects playng the Nash equlbrum strategy even when play s smultaneous rather than sequental. Ths paper s organzed as follows. Secton 2 gves the expermental desgn, and secton 3 presents the data. Fnally, secton 4 concludes. 2 The expermental games, treatments and procedures 2.1 The expermental games The game we study s very smlar to the standard publc good game (Fehr and Gächter 2000). At the begnnng of the experment, subjects are placed n groups of n subjects. They reman n the same group n all T > 0 perods of the experment. Each subject s assgned an dentfcaton number at the start of the experment, and ths number remans the same throughout the entre sesson. Fnancal returns are expressed n ponts, whch are converted to Euros at the end of the experment.

4 Subjects can nvest ponts n a publc account, but also n a prvate account. Investments n the publc account beneft all members of one s group, unless they are undone by other subjects n the group. All ponts n a subject s prvate account are hers to keep. c Indvdual contrbutons to the publc good are denoted by [ a, e], wth a 0 and e > 0. If a subject decdes to make a postve contrbuton to the publc good, we refer to hm/her as an nvestor, and the postve amount contrbuted s referred to as the nvestment. When a < 0, subjects can also decde to contrbute a negatve amount, whch mples that they ncrease the number of ponts n ther prvate account at the expense of the number of ponts n the publc account. Negatve contrbutons wll be referred to as clams rather than, for example, takngs, because negatve contrbutons can only be realzed n full f the amount of postve contrbutons s suffcently large. In a group, the net aggregate number of ponts contrbuted n C to the publc account s equal to c = 1. Clamants and nvestors are dentfed by φ = ( cφ ) φ 1 ndcator functon, where = f c < 0, and zero otherwse. The total amount C nvested n the publc account s thus equal to n Inv n ( φ ) c =, and the number of Cl C φ 0 ponts clamed s 1 c =. Negatve contrbutons are clams to the ponts nvested by others, and these clams may or may not be successful. If Inv Cl C = C + C 0, all clams are satsfed, and the net contrbuton to the publc good, C, s multpled by α and then dvded equally among all n group members. If Inv Cl C = C + C 0, < all contrbutons by the nvestors are undone by the negatve contrbutons of the clamants. The publc good s then not produced (mplyng that t yelds a zero payoff) and ( clams are ratoned accordng to a Cl φc ) / C clamant s share n the total clams made by all clamants. c Subjects thus choose ther contrbuton levels from the range [ a, e], and we mplement three dfferent treatments usng dfferent combnatons of a and e. The standard VCM game s mplemented usng (a,e) = (0,20), and two versons of the Clam game are obtaned settng (a,e) = (-10,10) and (a,e) = (-20,20), mplyng that an ndvdual s contrbuton s not restrcted to the non-negatve doman. The payoffs of every subject n any of these three treatments can be represented as follows. If C 0, = π e c Cα + / n φ{0,1} = (1a) e c f φ 0 = (1b) If C < 0, π = c Inv e + C f Cl φ = 1 (1c) C In the treatment where (a,e) = (0,20), (ndvdual) contrbutons cannot be negatve and hence 0 we have φ = for all and also Inv C = C 0. Each subject s payoff structure s thus gven by (1a). The maxmum number of ponts a subject can nvest n the publc good s equal to e. Any pont not nvested ( e c ) s put n subject s prvate account, and all subjects n a

5 Inv group receve C / n = α C / n ponts from the publc good ndependent of whether they themselves made a postve contrbuton to the publc fund, or not. Equaton (1a) s the payoff functon typcally used n the lterature on VCM (or Publc Good) games, and we mpose that α / n < 1 <to have socal dlemma. α ( ) In the treatments where (net) contrbutons can be negatve (.e., (a,e) = {(-20,20), (-10,10)}), payoff functon (1a) may stll apply, but only f the total number of ponts nvested s at least as large as the total number of ponts clamed (that s, f Inv Cl C = C + C 0, Cl where C may be smaller than zero). In that case, each subject receves Inv Cl ( α ( + ) ) = C C / n Cα/ n 0 ponts from the returns from the net contrbutons to the publc account, and all clams are satsfed. The number of ponts n a subject s prvate e c account s thus equal to, and whether ths amount s larger or smaller than e depends on φ 1 whether subject s a clamant ( = φ 0 ), or an nvestor ( = ). If the number of ponts ( Inv C ) nvested ( Cl C ) s smaller than the absolute number of ponts clamed, we have C < 0 and the publc good fals to be produced mplyng that all subjects receve a zero return φ 0 from the publc account. Those who nvested ponts n the publc good ( = ) only receve e c the number of ponts they put n ther prvate account ( e φ 1 ; see (1b)). Clamants ( = ) stll have ther endowment, e, and n addton they receve a share 0 / Cl < c 1 C of the ( Inv C ) postve contrbutons by the others ; see (1c). In all three treatments, (a,e) = {(0,20),(-10,10), (-20,20)}, we set α = 1.6, n = 4, and T = 25. π Gven these parameterzatons, the standard game-theoretc predcton are that = e for all n all three treatments. Backward nducton mples that all n-player vectors c contanng only non-postve contrbutons (that s, [ a,0] ) are Nash equlbra: all Inv subjects put e ponts n ther prvate accounts, and because C = 0, any pont clamed cannot be satsfed. In every perod there s a domnant strategy of nvestng zero when a = 0, and a weakly domnant strategy of clamng a n every perod n the treatments wth a < The expermental treatments For ease of reference, we label the three treatments (a,e) = {(0,20),(-10,10), (-20,20)} as VCM[0,20], Clam[-10,10], and Clam[-20,20], respectvely. The socally optmal payoffs n VCM[0,20], the standard Publc Good game, and Clam[-20,20] are the same and equal to 32. The man mpact of allowng subjects to undo the good works of others can be gauged from comparng play n these two treatments as the benefts to cooperaton, defned as the socally optmal payoff mnus the Nash equlbrum payoff, are the same. The two treatments dffer, however, n the (maxmum) temptaton to defect the dfference n payoffs when choosng to defect rather than to cooperate whle all other group members fully cooperate. In VCM[0,20] the maxmum temptaton payoff s 12 ponts, but n Clam[ 20,20] t s 24 ponts. To control for that, we also mplemented Clam[-10,10]. In ths treatment the socally optmal payoffs are 16 and hence smaller than n VCM[0,20] but the maxmum temptaton payoff s 12 as s the case n VCM[0,20]. Table 1 gves an overvew of the treatments.

6 Table 1 Overvew of the experments Treatment Socally optmal payoff Maxmum defecton payoff Groups Indvdual earnngs VCM[0,20] Clam[-20,20] Clam[-10,10] The expermental procedure The experments were all conducted at the CentER laboratory at Tlburg Unversty n the Fall of Subjects were students wth dfferent natonaltes and wth backgrounds n busness, economcs, law, or socal scences. No subject partcpated n more than one sesson. Each sesson lasted roughly forty fve mnutes. All decsons were medated va z- Tree (Fschbacher 2007). The nstructons of the experment were neutral, usng phrases lke contrbutons to a project that may beneft all partcpants n your group, and you can make clams to take out ponts from the project. The nstructons presented the payoff functon as well as some examples of how the payoffs are calculated. We dd not nform subjects about the Nash equlbrum or socal optmal play n the games. Before each sesson began, all subjects had to complete test questons. Once all subjects correctly answered all questons, the experment began. All partcpants were able to answer all questons wthout much dffculty. 3 Data analyss Fgure 1 presents the aggregate net contrbutons, averaged over all groups, for each of the three treatments. The pattern n VCM[0,20] s a replcaton of what s typcally found n standard publc good experments. Intal contrbutons are roughly forty percent of the total endowment, and the contrbutons declne as the game progresses. Strkngly, n the two Clam games the net aggregate contrbutons are very close to zero n the frst few perods, and roughly reman negatve throughout the rest of the nteracton. In Appendx A, we show the net aggregate contrbuton levels for each treatment per group, and n Table 2 we present average net contrbutons (expressed as the share of the maxmum possble contrbutons n the treatment) n the three dfferent treatments along wth the relevant test statstcs.

7 Fgure 1 Net aggregate number of ponts contrbuted n the VCM[0,20], Clam[-10,10] and Clam[-20,20] treatments n each of the 25 perods, averaged over all groups n the treatment. Table 2 Net aggregate contrbutons as a share of the maxmum possble group contrbuton (averaged over all groups wthn a treatment); standard devatons n parentheses. Average net contrbuton share Dfferences n average net contrbuton shares Clam [-20,20] Clam [-10,10] VCM [0,20] Clam[-20,20] VCM[0,20] Clam[-10,10] VCM[0,20] Clam[-20,20] Clam[-10,10] Averaged over all rounds (0.241) (0.264) *** (0.309) *** (0.131) *** (0.141) (0.122) Average frst round (0.241) (0.276) *** (0.137) *** (0.093) *** (0.104) (0.125) *,**,*** ndcate sgnfcant dfferences at the 0.10, 0.05, 0.01 levels, respectvely, based on standard t-tests. The results of the t-tests presented n the frst three columns Table 2 ndcate that averaged over all perods, net group contrbutons are only postve and sgnfcant n the VCM[0,20] treatment, and not n the two Clam treatments. Not surprsngly, the dfferences n average contrbuton shares between the clam treatments on the one hand and the VCM treatment on the other hand, are negatve, and hghly sgnfcant see the last three columns of Table 2. Ths table also shows that these dfferences already manfest themselves n the frst perod of the nteracton. In that perod, average contrbuton shares n Clam[-10,10] and Clam[-20,20] are already smaller than n VCM[0,20], and standard t-tests do not allow us to reject the null hypothess that the average contrbutons are zero n the two Clam games. Ths gves rse to our frst result. Result 1 Throughout the nteracton average contrbuton shares are much lower n the Clam[-10,10] and Clam[-20,20] than n VCM[0,20], and fal to be sgnfcantly postve even n the frst perod. Result 1 states that patterns of net contrbutons are n lne wth the predctons provded by standard game theory whether t also holds for ndvdual play, wll be addressed later. These results complement the nsghts obtaned by Khadjav and Lange (2011). Whle contrbutons are sgnfcantly dfferent from zero even n ther takng game (wth average contrbutons equal to 43% of the maxmum n perod 1 and 22% averaged over all perods), average net contrbutons n both our clam games are n lne wth the Nash equlbrum predcton of zero net contrbutons even n the early perods of the nteracton. Moreover, whle Khadjav and Lange fnd that the net contrbutons n the treatment that allows for both gvng and takng do not dffer from those n ther VCM treatment (as the respectve average contrbutons are 58% and 59% of the maxmum n the frst perod, and 36% and 38% averaged over all perods), the ntal contrbutons n our clam games are sgnfcantly lower than n the VCM game even n the very frst perod. Khadjav and Lange thus fnd that

8 changng the acton space from just gvng to (also allowng for) takng makes subjects less cooperatve on average, but the Nash equlbrum predcton of zero cooperaton s rejected n all nstances. Our experments show that f the good works of some can actually be undone by others as s the case n CO2 emsson reductons aggregate play s n lne wth the standard neoclasscal predctons. Predctng ndvdual behavor may requre modelng each agent s utlty functon, but f polcy makers only care about the aggregate outcomes, they can safely assume that all agents behave as f they are purely self-nterested n some crcumstances (when some can undo the good works of others) but not n all (n those crcumstances n whch contrbutons cannot be negatve). Let us now turn to analyzng ndvdual behavor. Economc theory predcts that not only the aggregate amount contrbuted s non-postve, but also that each ndvdual s contrbutons are non-postve as well. As s well known by now ths predcton s volated n VCM games, but the queston s whether ths predcton s also volated f one s good work can be undone by others as s the case n the Clam games. Table 3 presents the shares of subjects choosng postve contrbuton levels n the three treatments n all perods, n perod 1, and, arbtrarly, also n perod 20. Averaged over all perods, subjects n VCM[0,20] chose postve contrbuton levels (as opposed to contrbutng zero) n almost 60% of the cases, whle subjects chose postve levels (as opposed to zero or negatve contrbutons) n 24% and 35% of the nstances n the Clam[-20,20] and Clam[-10,10] treatments, respectvely. These percentages are all sgnfcantly dfferent from each other accordng to standard Fsher exact tests. Moreover, the drop n nvestor shares from perod 1 to perod 20 s much more pronounced n the two Clam games than n VCM[0,20]. Table 3 Share of subjects choosng postve contrbuton levels n the three treatments, n perods 1, 20 and n all perods, and the assocated Fsher exact tests. Share of subjects contrbutng a postve Sgnfcance of the dfferences n shares of subjects amount to the publc account contrbutng postve amounts n the three treatments a Clam [-20,20] Clam [-10,10] VCM [0,20] Clam[-20,20] vs VCM[0,20] Clam[-10,10] vs VCM[0,20] Clam[-20,20] vs Clam[-10,10] All perods 217 / / / 900 p= p = p = Perod 1 21 / / / 36 p = p = p = Perod 20 2 / 36 7 / /36 p = p = p = a p-values obtaned usng standard (2-sded) Fsher exact tests. We summarze these results as follows. Result 2 The frequency wth whch postve contrbuton levels are chosen n the frst perod s hgher n VCM[0,20] than n the two Clam games, and the dfference n frequency dstrbutons s even larger n the later perods. Result 2 ndcates that the rate at whch subjects cease to nvest postve amounts n the publc account, falls faster n the Clam games than n the VCM game. Comparng play n Clam[-20,20] and n Clam[-10,10], Table 3 also ndcates that sustanng cooperaton s

9 more dffcult when the temptaton to defect s stronger. Ths s nterestng because the average contrbuton levels were not found to sgnfcantly dffer between the two Clam games; see Table 2. We explore the mpacts of () hgher defecton payoffs and () lower cooperaton benefts n two steps. Frst, we analyze the mpacts on the extent to whch subjects who started the game wth the ntenton to cooperate (by contrbutng a substantal share of ther endowment n the frst perod), are wllng to contnue cooperatng. Second, we use regresson analyss to dsentangle the two effects for all subjects nvolved. In Table 4 we present the average contrbutons shares n perods 5-20 of those subjects who contrbuted 40% or more of the maxmum contrbuton level n perod 1. Let us refer to these subjects as prosocal ndvduals. Table 4 shows that on average, the contrbutons of these ndvduals are postve n both Clam[-10,10] and Clam[-20,20], but not sgnfcantly so. Also, the average contrbuton share of these prosocal subjects s much greater n Clam[-10,10] than n Clam[-20,20], but ths dfference s not sgnfcant ether (p = 0.40 accordng to the Mann-Whtney U test). Ths gves rse to the followng result: Result 3 Those subjects who nvested substantally n the frst perod of the two Clam games, are not found to do so n the later perods; ther average contrbuton shares are postve but not sgnfcantly dfferent from zero. In addton, the average contrbutons of these subjects are smaller when the temptaton to defect s hgher, but not sgnfcantly so. Table 4 Contrbuton shares, averaged over perods 5 to 20, of the prosocal ndvduals n the three treatments; standard devatons n parentheses. Average contrbuton share over Dfferences n net average contrbuton shares a perods 5-20 Clam [-20,20] Clam [-10,10] VCM [0,20] Clam[-20,20] VCM[0,20] Clam[-10,10] VCM[0,20] Clam[-20,20] Clam[-10,10] (0.431) (0.448) *** (0.363) ** (0.153) ** (0.165) (0.197) a p-values based on standard Mann-Whtney U test. *,**,*** ndcate sgnfcant dfferences at the 0.10, 0.05, 0.01 levels, respectvely. Hence, subjects dsplayng the ntenton to cooperate by contrbutng a substantal share of ther endowment n the frst perod, tend to behave prosocally n the remander of the experment too n the sense that they, on average, do not choose negatve contrbuton levels. But they stll act more or less n lne wth the game-theoretc predcton n that ther contrbuton levels are not sgnfcantly postve ether. Comparng Tables 2 and 4 suggests that the non-prosocal ndvduals tend to choose negatve contrbuton levels, and possbly more so when the temptaton to defect s larger, thus nducng pro-socal ndvduals to choose contrbuton levels that are, on average, not sgnfcantly dfferent from zero. In Table 5 we show the regresson results tryng to parse out the mpact, on average play, from () partcpatng n a treatment wth hgher or lower benefts of cooperaton, and () facng a hgher or lower temptaton to defect. We construct a dummy varable HBenfsCoop whch has value 0 for treatment Clam[-10,10] and 1 otherwse, and a dummy varable HTemptDefect whch has value 1 for treatment Clam[-20,20], and zero otherwse. Table 5 dsentangles the mpact of the two factors on the actual contrbuton level.

10 The ntercept reflects the average contrbuton level when the benefts of cooperaton and the temptaton to defect are both small. Hgher benefts of cooperaton rase the average subject s contrbuton share by 26 percentage ponts, whle a stronger temptaton to defect reduces t by 42 percentage ponts. Over tme, contrbutons fall, but they fall slower (faster) when the benefts to cooperaton (temptaton to defect) are hgher. Ths gves rse to result 4. Result 4 Averaged over all subjects, contrbutons tend to be greater the greater the benefts of cooperaton, and smaller the stronger s the temptaton to defect. Over tme, contrbutons tend to fall, and the declne s fastest when the temptaton to defect s large and the benefts of cooperaton are small. Table 5 The effects of hgher cooperaton benefts and stronger defecton ncentves on absolute and relatve contrbuton levels. a Contrbuton as a share of the maxmum possble contrbuton Constant * (0.0975) HBenfsCoop ** (0.108) HTemptDefect *** (0.0963) Perod *** ( ) HBenfsCoop nteracted wth Perod *** ( ) HTemptDefect nteracted wth Perod * ( ) N 2600 Adjusted R F a Results of a standard OLS regresson. Robust standard errors, clustered at the subject level, n parentheses. *,**,*** ndcate that coeffcents are sgnfcantly dfferent from zero at the 0.10, 0.05, 0.01 levels, respectvely. 4 Conclusons In ths paper, we test the effects of gvng subjects the opton to choose negatve contrbutons n a game that s otherwse dentcal to the standard Publc Goods game. Subjects have the possblty to make postve contrbutons, but they can also make negatve contrbutons

11 ncreasng ther own prvate payoffs at the expense of the sze of the publc good. We compare play n the standard Publc Goods game, VCM[0,20], to two versons of our Clam game. In Clam[-20,20] the benefts of cooperaton are equally hgh as n the standard VCM[0,20] game, but the temptaton to defect (defned as the maxmum defecton payoffs) are twce as large. In Clam[-10,10], the temptaton to defect s equally large as n the VCM[0,20] treatment, but the benefts from cooperaton are half as large. Allowng subjects to undo the contrbutons of others results n aggregate contrbutons that are not sgnfcantly dfferent from zero from the frst perod onward as predcted by standard game theory. But also ndvdual play s roughly as predcted by game theory even subjects who started the game wth the ntenton to cooperate (by contrbutng a substantal share of ther endowment n the frst perod), choose effort levels that are, on average, not sgnfcantly postve. The possblty that each subject can (partly) undo the good work by others, results n behavor that we typcally refer to as selfsh contrbutng zero to the publc good. Ths s not because humans only care about ther own welfare play n VCM[0,20] proves the contrary but because the strategc envronment s such that t does not ncrease group welfare to be generous. In those envronmental problems where the good works by some can be undone by others, modelng the ecologcal-economc system assumng other-regardng preferences may complcate the models wthout mprovng ther predctve power. References Andreon, J. (1995). Warm-Glow Versus Cold-Prckle: The Effects of Postve and Negatve Framng on Cooperaton n Experments. The Quarterly Journal of Economcs, vol. 110, pp Bardsley, N. (2008), Dctator game gvng: altrusm or artefact? Expermental Economcs 11: Bolton, G., and Ockenfels, A. (1998). Strategy and equty: an ERC-analyss of the Güth-van Damme game. Journal of Mathematcal Psychology, 62, Camerer, C. F. (2003). Behavoral game theory: experments n strategc nteracton. Prnceton: Prnceton Unversty Press. Charness, G., and Rabn, M. (2002). Understandng socal preferences wth smple tests. Quarterly Journal of Economcs 117, Chaudur, A. (2010). Sustanng cooperaton n laboratory publc goods experments: A selectve survey of the lterature. Expermental Economcs 14(1), Cherry, T. L., Frykblom, P., and Shogren, J. F. (2002). Hardnose the dctator. Amercan Economc Revew, 92, Cox, J., Ostrom, E., Sadraj, V., and Walker, J. (2013). Provson versus approporaton n symmetrc and asymmetrc socal dlemmas. Southern Economc Journal. 79(3), p Dana, J., Weber, R. A., and X Kuang, J. (2007). Explotng moral wggle room: Experments demonstratng an llusory preference for farness, Economc Theory 33(1), Engel, C. (2011). Dctator games: a meta study. Expermental Economcs, 14 (4), Fehr, E. and Gächter, S. (2000). Cooperaton and punshment n publc goods experments. Amercan Economc Revew, 90 (4), Fehr, E., and Schmdt, K. M. (1999). A theory of farness, competton and cooperaton. Quarterly Journal of Economcs, 114, Fredman, M. (1953). The Methodology of Postve Economcs, n Essays n Postve Economcs, Chcago: The Unversty of Chcago Press: 3-43.

12 Forsythe, R., Horowtz, J., Savn, N., and Sefton, M. (1994). Farness n smple barganng experments. Games and Economc Behavor, 6, Gächter, S., Renner, E., and Sefton, M. (2008). The long-run benefts of punshment. Scence 322, Keser, C. (1996). Voluntary Contrbutons to a Publc Good when Partal Contrbuton s a Domnant Strategy, Economcs Letters 50, Khadjav, M., Lange, A. (2011), Dong Good or Dong Harm: Expermental Evdence on Gvng and Takng n Publc Good Games, Unversty of Hamburg. Ledyard, J. (1995). Publc Goods: A Survey of Expermental Research. Prnceton Unversty Press. Lst, J.A. (2007). On the Interpretaton of Gvng n Dctator Games, Journal of Poltcal Economy 115(3), McCarter, M.W., D.V. Budescu and J. Scheffran (2011), The gve-or-take-some dlemma: An emprcal nvestgaton of a hybrd socal dlemma, Organzatonal Behavor and Human Decson Processes 116, Rabn, M. (1993). Incorporatng farness nto game theory and economcs. Amercan Economc Revew 83, Snn, H.-W. (2008). Publc polces aganst global warmng: A supply sde approach, Internatonal Tax and Publc Fnance 15(4), Stern, N. (2007). The Economcs of Clmate Change, Cambrdge Unversty Press, Cambrdge. Stoop, J.T.R., D.P. van Soest and J. Vyrastekova (2013). A Tale of Two Carrots: The Effectveness of Multple Reward Stages n a Common Pool Resource Game, n M. Prce and J. Lst (eds.), Handbook of Economc Experments and the Envronment, Cheltenham: Edward Elgar, forthcomng. van Soest, D.P. and J. Vyrastekova (2006). Peer Enforcement n CPR Experments: The Relatve Effectveness of Sanctons and Transfer Rewards, and the Role of Behavoral Types, Chapter 6 n J.A. Lst (ed.), Usng Expermental Methods n Envronmental and Resource Economcs, Cheltenham: Edward Elgar: Appendx A: In ths appendx, we show the contrbuton levels per group. Contrbutons per group n VCM[0,20]

13 Contrbutons per group n Clam[-20,20]

14 Contrbutons per group n Clam[-10,10] 18