Beating by hitting: Group Competition and Punishment

Transcription

1 Beating by hitting: Group Copetition and Punishent Eva van den Broek *, Martijn Egas **, Laurens Goes **, Arno Riedl *** This version: February, 2008 Abstract Both group copetition and altruistic punishent have been put forward as explanations for sustained cooperation in groups. Yet, punishent costs ay be detriental to a group s relative fitness in copetition with others. We investigate the dynaics of altruistic punishent when there is group copetition by conducting a series of experiental public goods gaes in which we systeatically vary the possibility for social coparison, group copetition and punishent. Our results indicate that copetition attenuates punishing behavior, but leaves contribution levels unchanged despite the relative lack of enforceent. JEL classification: C70, H41 keywords: experient, public goods, cooperation, punishent Both experiental evidence and casual observations of huan cooperation are well docuented, yet their origin constitutes a puzzle to scientists fro various disciplines. Recently, the echaniss sustaining costly altruistic behavior have been intensively studied. Altruistic punishent and group copetition are two iportant echaniss that have shown to corroborate cooperative behavior in social dileas (Nowak 2007). * corresponding author: evdbroek@uva.nl. CREED, University of Asterda, Roetersstraat 11, 1019WB Asterda, the Netherlands. We gratefully acknowledge ENABLE. We also thank Arthur Schra and participants at the Econoic Science Association 2007 in Roa, and IAREP-SABE 2007, Lyon, for useful coents. ** IBED, University of Asterda, Kruislaan 318, 1098 SM Asterda, the Netherlands *** Faculty of Econoics and Business Adinistration, Maastricht University, P.O. Box 616, NL-6200 MD Maastricht, the Netherlands

2 Hollywood discovered the tragedy of the cobination of these two institutions. In the ovie 'Eney at the gates' (2001), the Russians try to defend Stalingrad against the wellequipped Nazis. Soldiers who tried to flee were shot by the achine guns of their peers, who thereby reduced their own chances of surviving the battle. The experiental literature shows that costly punishent is one of the echaniss that can sustain cooperation over tie (Fehr and Gaechter, 2002). The ere presence of the opportunity to punish defectors reduces the level of free-riding in a repeated public goods gae, thus increasing the total group payoff (Fehr and Gaechter, 2000). Explanations for the evolution of costly punishent partially rely on this effect. Theoretically, groups where the nuber of punishers is sufficiently large will outperfor groups with fewer punishers (Boyd et. al. 2003). Moreover, recent experients with endogenous selection of institutions show that a population deliberately igrates to groups ipleenting punishent (Gürerk e.a. 2006). It is far fro clear, however, that such a regie indeed leads to higher individual payoffs (fitness) for the group ebers, since the detriental effects of costly punishent are considerable (Fehr and Rockenbach, 2003). The effect of group copetition on the perforance of strategies eploying costly punishent reains largely unknown. Boyd's et al. hypothesis that groups with any punishers will thrive relies on the arguent that selection against punishent is weak when punishers are coon. This presues that copetition will not alter punishent behaviour as such. With this paper we want to experientally address the question that Boyd ea (2003) raise: do people in the lab resort to punishent when they face copetition on outcoes? One aspect of group copetition is that individuals ay observe the choices of (ebers of) other groups. The effect of group observation and group copetition on contributions is inconclusive, but generally positive. Subjects contribute ore to a public good when the perforance of another tea is observed (Sausgruber 2005). Moreover, the lower contributions soeties observed in a copetitive public goods setting can, counter intuitively, ainly be attributed to choices by prosocial types (Grosser and Sausgruber 200X). Also, previous victories dapen individual efforts in subsequent rounds (Tan and Bolle 2006). 1

3 In both the copetitive and the single group setting, the punishent option raised contribution levels to 50 percent, although punishent levels were very low- even lower in the copetitive setting (Bornstein, Kugler and Goren, pers co.). These findings were explained by otivational abiguity of contributions- free riding can be seen as an attept to reach intergroup-cooperation. The strength of the ipleented copetition does not influence the increase in contributions uch (Bornstein, Gneezy and Nagel, 2002). Suarizing, for a prosocial person the otivation to contribute is unclear - by contributing to his in-group, he raises the incoe of the in-group ebers, but at the sae tie reduces that of the out-group ebers. Siilarly, it is unclear whether a person should punish; cooperation would be enforced through punishent, but the punishent can reduce their own payoff with double ipact. If behavior is unaffected by the introduction of group copetition, groups in which punishent is abundant will earn relatively less over tie. Do punishers foresee this and adjust their behavior? We want to disentangle the individual otivations for punishent and the change in the effect of punishent under copetition. These questions are addressed by systeatically coparing the effects of punishent under a regie of group observation and group copetition. 1 The public goods gaes and theoretical predictions Model and Paraeters Consider a standard public good gae. In each period each of the subjects in a group receives an endowent ω. Subjects decide how uch of their endowent to invest into a project (0 g i ω). Each onetary unit invested in the project yields a constant arginal benefit of a to every group eber. The payoff π i that subject i K receives is a function of the endowent ω, the contribution to the public goods gae g i, the individual arginal benefit a and the contribution to the public goods gae of the individuals in group K: πˆ = ω g i i + a k = 1 g k (1) Group interaction 2

4 The basic design of our experient consists of a 3-person public goods gae, repeated for thirty periods. Subjects were atched as partners and were not infored about the identity of the other group ebers or other players in the gae. We systeatically varied (1) the opportunity to punish fellow group ebers and (2) group copetition (no group interaction, group observation alone, and group observation and copetition) in a coplete 2x3 design. This lead to 6 treatent conditions (see table 1.1). no group interaction (n=3) group observation (n=6) group copetition (n=6) without punishent Nx (7 groups) Onn (6 groups) Cnn (8 groups) with punishent Np (6 groups) Opp (8 groups) Cpp (8 groups) Table 1.1 treatent conditions The Nx and Np treatent serve as control treatents, where one group of three subjects plays a public goods gae respectively with (Np) or without (Nx) punishent opportunities. In the group observation treatents (Onn and Opp), two groups learn in predefined periods the total group earnings of the group they have been paired with, without any payoff consequences. For the purpose of coparison between treatents these periods were randoly defined beforehand and the sae in all replicas and treatents. Subjects did not know at which periods a group interaction would occur, only that they occur with a given chance. During each of these group interactions subjects received inforation on the total group payoff in that period of both their own group and the group they were paired with. In the group copetition treatents (Cnn, Cpp), being paired with another group has payoff consequences: In a period with group interaction, a transfer t takes place fro one of the groups to the other. The payoff function for subject i K can now be written as: π i = ω gi + a k = 1 g k + t i K (2) with ti K being the transfer t to subjecti K. We assue that the transfer is a linear function of the difference in the two groups aggregate payoffs. Denoting groups by K and L (hence, = K = L ), these payoffs are given by Πˆ and Πˆ, the earnings before group interaction. Using a factor f to scale the ipact of group copetition this yields: K L 3

5 t i K Πˆ = f K Πˆ Conversely, the payoff for subject L j L is: (3) π = ω g + a g + t j j l l = 1 j L with t j L = f Πˆ L Πˆ K (4, 5) The conditions for a social dilea are et if 0 < a < 1 < * a. Punishent Punishent is ipleented by the possibility for subject i to subtract fro a fellow group eber, k, p ik points at a cost c, with an ipact of d per allocated point. As a consequence, the payoff function becoes π t i = ki + K i K ω gi + a gk c pik d p Πˆ = f K k = 1 Πˆ L k= 1 k= 1 ti with (6, 7) MPCR In the periods with group copetition, the payoff not only depends on the public goods gae, but also on group copetition. Because group copetition is incorporated by a linear function of the group difference in payoff (equation 3 and 5), the MPCR reains a constant. An increase in contribution not only leads to a negative return fro the public goods gae at the individual level, but also to a positive expected return fro group copetition, because the group payoff Πˆ increases. Rewriting the group payoff before group copetition, Πˆ K and Π, as a function of ˆi π ' and ˆ π j ' (eq. 1) and substituting in (6) we get: ˆ L = + qf πi ω gi + a gk c pik d pki ( a 1) gi g k= 1 k= 1 k= 1 i= 1 j= 1 j (8) where q denotes the probability with which group copetition occurs. The MPCR of the gae with group copetition is therefore given by: 4

6 π i ' g i ' = a 1 + qf ( a 1) (9) The social dilea is now bounded by the paraeters a > 1 (as before) and in addition qf a + ( a 1) < 1 We designed the experient to ipleent group copetition with equal aterial incentives for all treatents. In the treatent with group copetition, the MPCR s in periods with group copetition are different fro MPCR s of periods without group copetition. Since subjects in the copetition treatent could not predict in which rounds group copetition would occur, the expected MPCR in each period is given by equation 9. To keep arginal incentives equal, the MPCR s were equalized across treatents, i.e., π i a s were chosen such in the two treatents that the equation for the MPCR, = a 1, g equals equation 9. Given MPCR a in the treatent without group copetition, we chose a for the group copetition case such, that: qf a + a` = (10) 1 + qf i 2 Experiental design and procedure 2.1 Paraeters Paraeters for the public good were set to endowent (ω) = 20, MPCR (a) = 0.4, group size () = 3. The transfer factor between groups (f) was set to 3, eaning that each group eber of the losing group receives the difference in the two group s earnings fro a eber of the winning group. Groups et with a probability of q=0.2 for each period and group interaction periods were randoly defined beforehand at period 3, 6, 13, 17, 21 and 27. The punishent cost/ipact ratio was set at c:d = 1:3. To copensate for the change in incentives for cooperation as a result of group copetition as described above, the MPCR for the copetition treatents (a`)was set at (eq. 10). 5

7 2.2 Theoretical predictions With an MPCR between 0 and 1 (one of the conditions for the public goods gae to constitute a social dilea) the personal return fro investing into the public good is always saller than 1. Under assuptions of self-interest and rationality, subjects use MPCR values to consider their contribution and therefore contribute zero to the project. Since punishing lowers their payoff, subjects never resort to punishing and therefore never fear to be punished. With the above described paraeter set, copetition does not change these predictions. 2.3 Ipleentation of the gae In all treatents, subjects decide on the individual contribution to the public good and receive inforation about all group ebers decisions and the consequences for their personal earnings and their group s earnings. Every period of the gae consisted of a decision stage, a punishent stage (if applicable) and several inforation stages, where the nuber depends on the treatents. In the control treatent, inforation is provided about the contributions of all group ebers, the total return fro the project, the personal return fro the project, personal earnings, and the total earnings of the group. A personal bank account is updated throughout the gae and updated with ost recent earnings at the end of every period. In the punishent treatents an additional inforation stage is ipleented with inforation on punishent points involving the subject, the incurred costs and the payoff consequences. In the treatents with group interaction and observation, but only in the periods with group interaction, subjects also learn the total earnings of the group they are paired with, the difference with their own group (in the observation and copetition treatents) and the transfer of earnings resulting fro group copetition (in the copetition treatents only). 2.4 Subjects The experient was conducted at the CREED laboratory at the University of Asterda in the acadeic year of 2006/2007. A total of 229 subjects participated in 16 sessions, ostly undergraduate students at the University of Asterda. Participants ajored in econoics (34,1%) and in a variety of other fields. Their average age was 22 and 33% percent of participants were woen. Average earnings were euro for one hour (plus 6

8 5 euro show-up fee). Subjects were paid anonyously and no counication was allowed during the experient. The experient was coputerized and written in ztree (Fischbacher 2007). Written instructions in Dutch (see appendix 1 for translation) were provided to the subjects. We checked for understanding by eans of a questionnaire (appendix 3); subjects with incorrect answers or questions were individually advised. After the experient we acquired personal inforation and conducted a personality test before the anonyous payent took place. 3 Experiental results 3.1 Contributions, punishent and earnings Figure 1 shows average contributions per period for the different treatents; for contributions per group for respectively Cpp and Opp, see Appendix. The control treatent, Np, shows a pattern siilar to the findings of earlier punishent studies (FG), naely an increase in contributions at the beginning, followed by a stable tie period at approxiately 70 % of the endowent and an end gae effect. Result 1: Contributions do not differ between the copetition (Cpp) and observation (Opp) treatent with punishent. Mean individual contribution rates of Cpp (17.39) and Opp (18.08) do not differ significantly (Mann-Whitney: U= 21.00, z=-1.15, p=0.28). Contributions across rounds are depicted in Figure 1. Individual contributions in the first round differ significantly for Cnn (Anova, p=0.05) and stay considerably lower over all rounds (average = 10.54, Mann- Whitney Cnn-Cpp: U=1, z=-3.256, p<0.01)* 3. Contributions in the control treatent Np stabilize at a lower level (average = 14.96, (50 %, as siilar to earlier findings) copared to the treatents with group interaction, however not significantly so (Mann-Whitney Np- Opp: U= 23.00, z = -0.13, p=0.95). - insert graph 1 about here - 3 In all statistical tests the group is the unit of observation, unless stated differently. For the group interaction treatents (Cpp,Opp,Cnn,Onn), a statistical group consists of 6 subjects, because their actions are interdependent; for the Np treatent, a group consists of 3 subjects. 7

9 Opp Np Cpp Cnn Graph 1. Average contributions in Observation with punishent (Opp), Copetition with punishent (Cpp), Copetition without punishent (Cnn) and the control treatent with punishent only (Np). Further analysis of the aggregated contributions revealed a difference between the groups winning and losing the copetition (with winning groups defined as groups with on average the highest contribution of the two over the first 26 periods). However, we did not find a difference between the contributions of the winning groups in Cpp and Opp (Mann- Whitney, p=0.22), nor between the losing groups in Cpp and Opp (p = 0.29). Suarizing, the contributions in the copetition and the observation treatents are not significantly different fro each other. Result 2: The nuber of punishent points allocated per person is higher in Opp than in Cpp. This is ainly due to an increase in punishent in the groups with lower contributions. The total nuber of punishent points allocated per person in Opp (14.98) is alost three ties the aount of punishent points in Cpp (5.71, see graph 2), although this is not significant at the group level (MW: U = 19.00, z = -1.36; sig = 0.195; edian test not significant). Dividing the copeting groups again according to their contributions in the winning and the losing groups reveals that the losing groups alost copletely account 8

10 for the observed difference in punishent between the treatents. The average nuber of allocated points per person over 30 periods is for the winning groups: Cpp: 0.85 points, Opp: 1.31; for the losing groups, Cpp: 2.96, Opp: 8.68 (Mann-Whitney U = 185, z =-2.12, p=0.034). - insert graph Cpp, Opp, Np punishent points Opp Np Cpp Graph 2. Punishent points allocated per person over rounds in Observation with punishent (Opp), Copetition with punishent (Cpp) and the control treatent with punishent (Np). Result 3: Individual earnings after 30 rounds are slightly but not significantly higher in Npp (average = 19.46) than in Cpp (average = 19.27; Mann Whitney U = 28, z = , p = 0.674). Average earnings in Np are 19.82; in Cnn Main result: Copetition akes punishent ore effective copared to punishent under observation. Three findings constitute this. 1. Contributions do not differ between the copetition (Cpp) and observation (Opp) treatent with punishent; 2. Punishent levels are lower in Cpp than in Opp; 3. As a consequence of a and b payoffs are higher in the copetition treatent. 9

11 In the treatents with group copetition, less punishent (significantly less in the losing groups) leads to siilar contributions and final earnings copared to when there is only group observation. This effect can have two causes. Firstly, people perhaps assign fewer punishent points because the copetition by itself keeps up contributions. In order to test that effect, we conducted another control treatent (Onn) with group observation but without punishent. Contributions here should be lower than in Cnn if the above conjecture were true- however, we did not find a significant difference between the Cnn and Onn treatents (average contribution in Onn was 8.19; Cnn-Onn Mann-Whitney U = 23.00, z = -0.95, p = 0.35). Apparently, the interaction of group observation and the ere opportunity for punishent drives up contributions, even without substantial actual punishent taking place. A second explanation for the increased contributions in the copetition treatent is that the punishent points that are received have a larger ipact on subsequent contributions. To differentiate between these two factors that constitute the results, we now focus on punishent behavior. First we consider individual deterinants of punishing, and then we analyze the effects of punishent on behavior in subsequent rounds. 3.2 Punishent behavior Individual factors deterining punishent behavior The observed decrease in allocation of punishent points in the Cpp copared to the Opp treatent can arise for two reasons. Firstly, the nuber of punishent points received is generally increasing with the positive difference in contribution between the punisher and the punished. However, we found a lower variance in the contribution of participants per group (3 subjects) in Opp (8.78 points) than in Cpp (9.94 points; MW U = , z = , p = 0.08), so the differences in variance cannot account for the differences in punishent. As a second explanation for the decrease in punishent points, copetition could dapen the punishing in response to the differences in contributions ore in Cpp than in Opp. - Insert graph Pairwise Differences here - 10

12 [-20,-14][-14,-7] [-6,-1] [0] [1,6] [7,13] [14,20] Np Cpp Opp Graph 3. Pairwise differences of contributions between punisher and punished, with resulting average punishent points allocated per category, in the copetition treatent (Cpp), the observation treateent (Opp), and the control treatent (Np). In the control treatent (Np), allocated punishent points increase with the (positive) difference in contribution between the punisher and the punished. This increase turns out to be uch higher in the observation treatent (Opp, see graph 3). Coparison without copetition apparently aplifies punishent; with copetition (Cpp), this effect is dapened. Result 4: More punishent takes place in Opp than in Cpp because copetition extenuates the allocation of punishent points in reaction to differences in contribution. See appendix for regressions with individual factors deterining punishent behavior. The odel including treatents, period 1 and 2, negative deviation of punished subject to punisher, the interaction ter of this negative deviation with treatents and the su of contributions of all group ebers explains 14% of the allocated punishent points to soeone (Wald Chi2 = ; p < ). The interaction ter of the negative deviation with the Opp treatent is the strongest predictor of this group. Individual reactions to punishent 11

13 The effects of sanctions on contributions in the subsequent round differ rearkably between the treatents (see graph 4). In the treatent with copetition, the change in contribution in the last round increases with the nuber of punishent points received; for the other treatents however, we do not observe such an effect (for regressions, see Appendix). 12 change in contr next round [0] [1,3] [4,6] [7,10] [11,15] [16,20] punishent points received np npp cpp Graph 4: change in contribution in next round as a result of the punishent points received for Cpp (copetition), Opp (observation) and Np (control). Result 5: in Cpp the contributions are increasing with the level of punishent in the round before. Discussion This paper investigated whether the detriental effects of punishent could be overcoe in a group copetition setting. We find that copetition akes punishent ore effective- although copetition attenuates the nuber of allocated punishent points, their ipact on contributions in the next round is higher. Copared to the observation treatent without onetary consequences (Opp), contribution levels and earnings in the treatent with copetition (Cpp) are coparable despite this lack of enforceent in the latter. 12

14 References Bornstein, G. and Gneezy, U (2002). Price Copetition Between Teas. Experiental Econoics, Vol 5, 1, Bornstein, G. (2003). Intergroup Conflict: Individual, Group, and Collective interests. Personality and Social Psychology Review 7(2): Bornstein, G., Gneezy, U, Nagel, R (2002). The effect of intergroup copetition on group coordination: an experiental study. Gaes and econoic Behavior 41: Bornstein, G., Kugler T. and Goren H. (not written yet) The Effect of Punishent on Cooperation in Single Group and Inter-group PD gaes. Bowles, S. and H. Gintis (2004). The evolution of strong reciprocity: cooperation in heterogeneous populations. Theoretical Population Biology 65(1): Boyd, R., Gintis, H. Bowles, S., and Richerson, P.J. (2003). The evolution of altruistic punishent. PNAS 100, Egas, M., Riedl, A. (2008). The econoics of altruistic punishent and the aintenance of cooperation. Proc Roy Soc B. Fischbacher, U. (2007). z-tree: Zurich Toolbox for Ready-ade Econoic Experients, Experiental Econoics 10(2), Fehr, E., Gaechter, S. (2000). Cooperation and punishent in public goods experients. AER 90: Fehr, E., Gaechter, S. (2002). Altruistic punishent in huans. Nature 415: Grosser, J., Sausgruber, R. (2005) Effort externalities and social nors in the workplace. ieo Gunnthorsdottir, A. and Rapoport, A. (2006). Egalitarian vs. proportional profit-sharing rules in ulti-level collective action probles. Organizational Behavior and Huan Decision Processes, 101, Gürerk, O, Irlenbusch, B, and Rockenbach, B. (2006) The Copetitive Advantage of Sanctioning Institutions. Science 312 (5770), 108. Nalbantian, H. R., Schotter, A. (1997). Productivity under group incentives: an experiental study. Aerican Econoic Review 87(3): Sausgruber, R. (2005). Testing for tea spirit- an experiental study. Tan, J. and Bolle, F.(2007). Tea Copetition and the Public Goods Gae, Econoics Letters, Vol.96 (1),

15 Appendix Iteration 1: log likelihood = Rando-effects tobit regression Nuber of obs = 3599 Group variable: trtnsgrp Nuber of groups = 40 Rando effects u_i ~ Gaussian Obs per group: in = 89 avg = 90.0 ax = 90 Wald chi2(10) = Log likelihood = Prob > chi2 = puntoown Coef. Std. Err. z P>z [95% Conf. Interval] np cpp opp per per negdev negdevxnp negdevxopp negdevxcpp socontr _cons /siga_u /siga_e rho