Endogenous Shifts Over Time in Patterns of Contributions in Public Good Games

Transcription

1 Endogenous Shifts Over Time in Patterns of Contributions in Public Good Games Sun-Ki Chai Dolgorsuren Dorj Ming Liu January 8, 2009 Abstract This paper studies endogenous preference change over time in a public good environment as an explanation of cooperative behavior. We investigate experimentally the role of (i) uncertainty and (ii) incentives for members of group size four. We compare the result to the benchmark with no uncertainty and no incentives. Our results show that (a) uncertainty in private account increases individual contribution level; (b) with uncertainty in public projects individuals contribute less, but the total contributions stay stable; (c) with incentives the outcome is close to the social optimum. JEL classification codes: C7, C91, C92, H41, D81. 1 Introduction When markets unable to provide socially optimal level of public parks, roads, libraries, public health how existing institutions or social norms perform in provision of those goods? Does optimism and voluntarism resolve the social dilemmas? This paper presents a number of experiments to test preference Corresponding author Department of Sociology, University of Hawaii at Manoa, 2424 Maile Way, Honolulu, HI sunki@hawaii.edu Department of Economics, University of Hawaii at Manoa, 2424 Maile Way, Honolulu, HI dolgorsu@hawaii.edu Department of Economics, University of Hawaii at Manoa, 2424 Maile Way, Honolulu, HI mingliu@hawaii.edu 1

2 change over time and endogenous formation of cooperation in voluntary contribution mechanism. It has been long debate on cooperation and selfish behavior in voluntary contribution mechanisms. Standard economic model predicts that selfish players would contribute nothing in public good games while other-regarding models predict some level of cooperation due to altruism, group behavior and social norms. Various theories of static social preferences, such as reciprocity (Rabin 1993, Dufwenberg and Kirchsteiger 1998, Falk and Fischbacher 1998), difference/inequity aversion (Bolton and Ockenfels 2000, Fehr and Schmidt 1999), and altruism/social welfare (Andreoni and Miller 2001, Charness and Rabin 2002) extend classical model, explain cooperative outcomes. Experimental evidence reveal that possibly all range of actions is available in public good environments once subjects walk in to the lab varying from zero contribution to the contribution of entire endowment. In general, about percent of group optimum can be achieved (Ledyard 1995). It has been established that at initial stages subjects contribute half of their endowment and contributions decline toward the end of the game with more repetition (Isaac, Walker and Thomas 1984). This might be due learning, or strategic attempt to signal or punish others. However, careful control of environment in laboratory may induce variations in contributions. Ledyard (1995) summarizes various factors that may influence cooperation: group size, marginal payoff, experience, threshold, rebates, communication and uncertainty. Ambiguity is considered as a situation when player is uncertain about the other s contributions. In a public good game with strategic substitutes and positive externality and where players display concave utility function ambiguity increases contribution (Eichberger and Kelsey 2002). Various uncertainties have been introduced into analysis such as uncertainty about the other s degree of altruism (Palfrey and Rosenthal 1988); uncertainty about the other s contribution cost (Palfrey and Rosenthal 1991); uncertainty about other s valuation of public good (Menezes et al. 2001); unknown pool size (Budescu et al., 1995); and unknown threshold (Ramzi Suleiman 1997, Nitzan and Romano 1990). Gradstein et al. (1993) showed that artificial randomness in prices alleviates the free rider problem and increases welfare. Keenan et al. (2006) extend a view that the price uncertainty reduces free-riding. Experiments report uncertain group payoffs reduce individual contributions but not the group contributions (Dickinson 1998). Dale (2004) provides more evidence on a fixed-prize lottery structure that induces higher level of public good than does a revenuedependent lottery. 2

3 None of these existing studies focus on endogenous change of preferences over time. Depending on the audience, it would also be useful to analyze explanations from economic sociology and exchange theory, but it is fairly straightforward to show that these are not really designed to explain shifts over time in contributions. Dynamics explanations would also be discussed, but much of existing work does tend to focus on natural selection arguments, in which fixed types are removed or added to the population. This includes Ostrom (2000), and also theoretical work by Bowles and Gintis et al. (2003), Rajiv Sethi (2006), and Bendor, Mookherjee, and Ray (2001). This could not explain change within among a group of subjects that remains unchanged throughout. Learning models, on the other hand, examine repeated games in which high levels of cooperation could be one of many equilibrium strategies due to reputation effects and possibilities for punishment, and hence do not require social preferences. Carpenter (2005) shows that preferences do change and affected by institutions where people interact with each other. He finds that reducing anonymity increases pro-social behavior while competition and markets reduce other regarding preferences of participants in ultimatum games. However, his study have not been concerned about the uncertainty effect. The main purpose of this paper is to examine preference change over time as an explanation of cooperation in a simple public good environment. In particular, we test following propositions using controlled experiments: (i) contributions to public goods should remain stable over time if the effect of one s own actions on payoffs is completely predictable and others actions are not known; (ii) if a subject faces uncertain personal benefits for contributing to a public good, while the public benefits are certain, this will tend to increase the subject s long-term willingness to contribute to the public good. This will be true regardless of their overall past level of benefits, and thus does not simply reflect a concave valuation function for their own payoff; (iii) subjects who vary their levels of contribution to a public good will tend to induce greater cooperation among their partners than those who contribute the same amount each period, assuming that the mean contribution of each type of subject is the same. Next section describes model and its predictions. Section 3 explains experimental procedures and design. Section 4 presents the results and section 5 has discussion and concluding remarks. 3

4 2 Theoretical Predictions We adopt a standard public good model and introduce uncertainty in finitely repeated game with finite number of players. By backward induction technique Nash equilibrium of finitely repeated game is identical to the equilibrium in one-shot game (Benoit and Krisna 1987). Hence, we discuss equilibrium of one-shot games. 2.1 Standard public good game Standard public good game by default has no institutions; the physical environment and institutional environment coincide. This model is classical in a sense that players assumed to be selfish and identical; players have no parameters attached to the utility of other decision makers. In particular subjects are allocated into groups of size N (our case is N=4). Each subject with endowment, e, decide on the amount of contribution to the group exchange, c i, i = 1,..., N, which will be used to produce public good. The rest of endowment goes to the individual exchange, e c i, which will be consumed individually. Let A be the revenue from each token invested in individual account to the subject alone. On the other hand each token invested into group account generates a payoff B to every member in the group. We consider a case when B < A < NB, where each subject has a dominant strategy to contribute nothing. Then each player profit is given by π i = e c i + [2 c i /N]. Here B=2 c i /N and A = e c i, where N = 4 and constant two represents the efficiency factor. From the first order condition we find the equilibrium π i c i contribution by each person: = < 0. Since the marginal payoff 2 from not contributing (1) is higher than the marginal payoff of contributing (1/2), player contributes nothing, c i = 0. The following is established by Isaac et al. (1985). Proposition 1 Selfish Nash equilibrium with homogeneous types and complete information determines the contribution by each subject: c i = 0. Hence the public good is underproduced with voluntary mechanism. 2.2 Social Optimal Social planner maximizes the sum of the payoffs: 4

5 max C πi = N e N c i N N c i ; (1) where 0.5 = 2/N is a marginal per capita return and C = N i=1 c i = N c i, i = 1,..., N. π i = N > 0; (2) C hence with N = 4 benefit from group exchange is greater than marginal benefit from individual exchange, individual contributes, c i = e. Proposition 2 From the society point of view it is optimal to contribute entire endowment to the public good provision. Hence, public good is provided and total contributions are given by C = N e. 2.3 Competing theories Classical model with selfish players assumes that people do not care about well being of other members of society. However, field experiments and field studies have shown tremendous amount of cooperation in public good environment. Citizens vote in elections, donate to the public radio and various public projects, voluntarily organize themselves to collectively benefit from their actions such as labor unions, professional associations. Consider following public good game, where the private account has uncertain feature. Classic Model with Hybrid Exchange: There is an element of uncertainty in the individual exchange such that with fifty percent probability it may stay as individual exchange or with fifty percent probability it may turn into modified version of group account. Modified group exchange operates in a similar way to group exchange, except that, instead of providing cash equivalent to half of the total amount invested to each member of the group, only one-quarter is given. In this model individuals choice is determined by maximizing: max επ i = (e c i ) 1 N c i (e c i ) 1 N c i ; (3) i=1 i=1 FOC: επ i = 1 c i < 0 (4) 8 5

6 As you can see marginal payoff from contributing (1/2) is lower than marginal benefit from not contributing (5/8). We could present above result in general form with probability of states denoted by p (0, 1): FOC: max c i επ i = (e c i ) p N N (e c i )(1 p) c i ; (5) i=1 i=1 επ i = p + p < 0 (6) c i 4 where p is a positive number. Individual will contribute nothing if the probability of state is greater than one third (1/3). Therefore, in Nash equilibrium pure self centered individual s contributions are zero, c i = 0, if p > 1/3 and c i > 0 if p < 1/3. Proposition 3 Suppose subjects face the uncertainty with respect to the return from the private account. Due to the lower return from modified account compared to the public account players will accommodate more of their resources into latter one if and only if the probability for hybrid exchange to stay as individual exchange is low enough, p < 1/3. Therefore, with the probability of the hybrid exchange to become an individual exchange equal to 1/2, self-regarding subjects will not contribute, c i = 0. Classic Model with Shared Random Exchange: Suppose public project has an uncertain payoff structure as follows. One member is chosen at random among the four members of the group, and each member of the group receives an amount equal to twice the chosen person s investment, regardless of what their own investment was. The payoff in this condition is given by: max c i επ i = (e c i ) + 2 [ 1 4 c i c j c k c m]; (7) FOC: επ i c i = < 0 (8) 6

7 Marginal return from private account (1) outweighs the return from public account (1/2). From individual point of view it is in her best interest to contribute nothing to the public account, c i = 0 1. Proposition 4 Suppose public project has uncertain element such that one person s contribution level randomly selected and each member receives twice of this amount. When the payoff from the public exchange is no certain individuals devote less of their resources to the public project. In this equilibrium with self-regarding individuals free riding is complete, c i = 0. Classic Model with Shared Maximum Exchange: We incentives the provision of public good in such a way that it is a dominant strategy to contribute. Suppose every token invested in shared exchange will earn two cents for every member of the group, not just the person who invested it, then each player maximizes: where i = 1,.., N. FOC: max c i επ i = e c i + 2 max(c i ); (9) επ i c i = > 0; (10) The marginal return from not contributing is one, while marginal benefit from contributing is two. Hence individuals best choice falls into the contributing to public good with positive amount. Proposition 5 With the incentives to contribute to the public good subjects contribute entire endowment. Thus, in equilibrium c i = e. Coherence Model: Analysis of preference and belief change and action in coherence model centers around three central concepts, decidability, doubt, and coherence. Decidability refers to the existence of an algorithm that allows an individual to determine optimal choices. Doubt refers to the expected gap between the utility provided by a chosen strategy and that provided by the optimal available strategy under each disposition of fates. Decidability and doubt may be analyzed in relation to choices over specific contingencies, 1 This game retains social dilemma issue as long as contributions of the randomly selected person to the public account are higher than e/4. Recall B < A < NB 7

8 while coherence is always be a property of a rule base as a whole. Coherence describes a condition in which, given preferences and belief, an individuals choice set over all periods is decidable and doubt over a chosen strategy is equal to zero (Chai 2001). Coherence Model with Hybrid Exchange: Assume for simplicity two possible states of nature in our hybrid VCM. State one: suppose hybrid exchange turns into modified group exchange, then marginal return from the hybrid exchange is 1/4 which is lower than the return from the public exchange (1/2). In this state the best payoff is 2e if everyone contributes to the public exchange rather hybrid. State two: If individual exchange stays as it is, then the best outcome for the selfish person would be if he/she free rides (contributes nothing) while all others contribute. In this case free rider earns 2.5 e. When all members free ride, everyone s payoff equal to e. For the altruist person the best outcome would be if all contribute to the public account in which case everyone will earn 2e; in the worst case cooperator earns 0.5e. In this state maximum non-cooperative payoff, 2.5e, is greater than the cooperative maximum payoff, 2e. Hence for free riders it is best to free ride and for cooperator the best choice would be to cooperate since altruist has higher utility when the total group payoffs are higher. In this model individuals choice is determined by minimizing her doubt over all possible states by picking up action that generates the highest utility and minimum regret: min u i,p s d i = s [u(s, a ) u(s, a)] p(s) (11) The utility is determined by transformation of payoff functions: u(s, a) = [π i + γ i π j ](1 h i ), j i, (12) i j Here γ i and h i are the group and grid attributes. The individual payoff in this game is given by: π i = [(e c i ) where p(s)=1/2. FOC: N i=1 c i )] [1 4 N N (e c i ) i=1 i=1 c i )] 1 2 ; (13) π i c i = 1 2 [ ] < 0 (14) 8

9 Marginal benefit in state 2 is higher than the marginal benefit in state 1, (1/2 > 1/4). Cooperator will contribute in public account due to intrinsic valuation of the public good which benefits everyone. Unlike self-regarding individual will contribute in order to avoid uncertainty in hybrid exchange if the probability of the hybrid exchange stay as an individual exchange is low enough, i.e. p 2 /p 1 < 1/2. If this holds in coherence equilibrium rational individual s contributions are positive, c i = e. Proposition 6 Suppose subjects face the uncertainty with respect to the return from the private account. Self-regarding players will accommodate their resources into public account if and only if the probability of the hybrid exchange to stay as individual exchange (p 2 ) is low enough, p 2 /p 1 < 1/2. Individuals with other-regarding preferences (cooperator) will accommodate their resources in the public account because it generates higher benefit to the group as a whole. See Appendix A for detailed case. Coherence Model with Standard condition The maximum available surplus reached again when individual contributes nothing toward the public project while others contribute positive amount. In this case individual s payoff is at 2.5 e. When all individuals contribute, everyone gets (2 e). The individual s choice is determined by: min u i,p(s) d i = S [u(s, a ) u(s, a)] p(s); (15) where j = 1,.., N. The payoff transformed utility function incorporates cultural attributes in the following way: FOC: N N 1 N u(s, a) = [e c i c j + γ i (e c i c j )][1 h i ]; (16) j=1 i j j=1 N π i = [e c i c j ]; (17) j=1 π i c i = [ ] < 0; (18) Other-regarding individuals best off by contributing to the public good since regret is lower in this case. See Appendix B. However, self-centered 9

10 individual places low value to others payoff, hence would not contribute to the public account. Thus, coherence model predicts contribution to be nonzero, c i > 0 for cooperator and zero for self-regarding individuals, c i = 0. At the same time shift in preferences in the hybrid treatment and cooperation may remain in sequence following standard treatment, c > 0 such that all types contribute. Coherence Model with Shared Random Exchange: In this treatment the public account become more risky in such a way that randomly selected person s contribution determines the group benefit from the shared random exchange. In this case public account may benefit everyone or may not. Classic model predicts rapid decline in contributions in this situation. Contrary, coherence model predicts increase in contributions over time. Individual minimizes difference between the best available surplus for her and actual surplus she may end up over all possible contingencies. The maximum available surplus happens when the person free rides and another person who contributes her entire endowment will be randomly selected among the group. The payoff in this case is equal to (e + 2 e). On the other hand if everyone contributes entire endowment, then uncertainty vanishes and for sure everyone gets twice her endowment, 2 e. The actual payoff individual getting is e in all states, if she free rides and everyone else does. There are many others states, where the best payoff for the individual lies between (0) and (e + 2e). Minimum regret occurs if altruist person contributes and selfish ones do not contribute because public account became more risky in this game. The payoff for individual is given by: π i = (e c i ) + 2 c i 1 4 ; (19) FOC: π i = p [ 1 + 1/2] < 0 (20) c i Assume that subjective probabilities of being selected are identical and equal to 1/4. For the cooperator (high-groupness) doubt would be minimized if contribution is greater than zero. Therefore, contributions will remain low since only cooperators contribute. Hence in coherence equilibrium, self-regarding (low-groupness) subjects do not contribute, c i = 0 and only cooperators contribute, c i > 0. Coherence Model with Shared Maximum Exchange Suppose the maximum contribution will be selected and everyone in the group will receive 10

11 twice this amount. The maximum available surplus occurs again when individual contributes nothing and others contribute. One s payoff is at (e+2 e). However, if the person contributes her entire endowment the payoff of 2 e is guaranteed for sure regardless of others actions. Individual minimizes the doubt over all states and the payoff are given by: FOC: π i = (e c i ) + 2 N max(c i); (21) π i c i = [ 1 + 2] > 0; (22) Here contributions will start with low level since this treatment follows from shared random treatment. However, individuals will have strong incentives to contribute to the public account because marginal return is twice their investment while in random treatment return is smaller ( 1 < 2). Thus, 2 in coherence equilibrium all types will contribute c i = e. 3 Experiment Design We report the results of computerized 2 experiments of a linear public good game, which is closely relates with previous papers. This study involved 104 undergraduates and graduate students from University of Hawaii at Manoa. Subjects received 10 dollars for participation and earned on average additional money of 17.5 dollars. Experiments took one hour to run. Subjects have seated separately from each other in lab computer terminals and were randomly grouped in four. They told that this group will remain the same throughout the experiment. No communication was allowed. Identity of other subjects in their group was unknown except the last session where only one group did come to the session. The instructions were provided in verbal and written format before players accessed computer entry. See Appendix 1 for instructions. Each player had an endowment of 50 tokens to invest in two exchanges: Individual and Group. We conducted four treatments in two designs (See Table 1). Design one involved 52 students and included two treatments: hybrid treatment (treatment 1) followed by the standard public good game (treatment 2). Hybrid 2007). 2 The experiment was programmed and conducted with the software z-tree (Fischbacher 11

12 treatment had hybrid and group exchanges where former was designed in a way that with fifty percent probability the individual retains one hundred percent of her investment and with fifty percent probability each member of the group gets quarter of the aggregate investment of all individuals. In other words hybrid exchange turned either into individual exchange or modified group exchange with known probabilities. Hybrid treatment consisted of a ten period finitely repeated game where subjects know the effect of their own actions on their payoff and they receive full feedback on the outcome including total investment in each account, individual investments in the group exchange, own payoff in total and subdivided into accounts and the probability of state for the hybrid account. Hybrid treatment had purpose to test whether uncertainty in the payoff structure from individual exchange would induce higher level of contributions over time in the group exchange. Hybrid treatment was followed by a ten period of finitely repeated standard public good game where after each round participants had feedback on the total contribution level, individual contributions, own split of endowment into individual and group exchange, her payoff from both accounts. In addition we test whether cooperation obtained in hybrid treatment would continue to sustain in the standard treatment. Evidence on cooperation in hybrid treatment through ten periods will indicate endogenous preference change. The second design involved another group of 52 students and consisted of two treatments that both had individual and group exchanges. However, group exchanges in two treatments differ in the following way. Shared random treatment (treatment 3) had a group exchange where one person is chosen at random, and each person in the group receives twice this person s contribution. Contrary in the shared maximum treatment (treatment 4) the maximum contribution is chosen and each person in the group receives twice this person s contribution. Each treatment lasts ten periods and groups had a partner matching. Basically, here we test whether risk factor in group exchange will prevent rapid declines in contribution levels. Also we test if this decline drops in the last ten rounds of shared maximum treatment where individuals have much more incentives to contribute. Therefore, with two consequent treatments played by the same subject we have within-subject comparison in addition to across-subject comparison. See Table 2 for sessions. There were thirteen groups of four people involved in both designs during eight sessions ran in two consecutive days. To test the spillover effect we reversed the ordering of treatments in last four sessions that include half of population involved. Standard treatment (2) followed by 12

13 hybrid treatment (1) and shared maximum treatment (4) had followed by shared random treatment (3) in reverse design. In all treatments individual contributions were listed in a descending order so that there was no possibility to reveal identity of the individuals from the contributions. We employed neutral language so that word investment used instead of contribution. Also history table of previous play has been provided in each period. To insure the understanding of payoffs involved in the experiment subjects completed the quiz and two practice periods with feedback were conducted to make them familiar with the software. After the experiment questionnaire was given to bring out participants strategies and opinions about the experience. 4 Results 4.1 Hybrid Exchange We use the standard treatment as a benchmark and compare with the experimental results from the hybrid experiment. Result 1 When individual exchange had probabilistic structure there is a clear increase in the contribution levels. The average contributions in hybrid treatment were highest among all treatments. Efficiency was higher than in the shared random and standard treatments. Support, Table 3 and 4, Column 2 Contribution level: Individual decisions were highly dispersed in the action space varying from 0 at minimum to 50 at maximum. Overall 66 percent of data are within the interval [25; 50] and 46 percent of individual actions are above 40. Out of all actions 31 percent were equal to the entire endowment of 50 tokens. The mean of contributions across the groups was 30.5 which is no different from a sixty percent of the endowment (p-value for t-test is ). Wilcoxon-Mann-Whitney rank-sum test suggests higher contributions with hybrid exchange than with standard treatment (p-value=0.0378). In terms of dynamics contributions stay pretty much at the same level in hybrid treatment. Wilcoxon rank-sum test shows no difference between average contributions in round 1, 5 and 10. See Table 4 for details. 13

14 Efficiency: On average efficiency was 80.5 percent of the maximum surplus available as compared to the Nash equilibrium level of 50 percent. Efficiency ranged across sessions from minimum of 72 to maximum of 96 percent. Although efficiency in hybrid treatment were the same across periods and did not drop toward the end. Therefore, in the hybrid treatment uncertain nature of the individual account induces preference change toward the public account for self-regarding subjects. This increases the level of contributions in the public exchange and efficiency as well. We know that cooperative subjects in any case minimize regret by choosing public account because their utility positively related with the other s payoff in the group. Thus, uncertainty in hybrid exchange supports cooperation in the public good situation. 4.2 Standard game Result 2 In line with standard model prediction free riding exists and full surplus has not been absorbed. In line with coherence model group contributions are far from zero. However, average contributions and efficiency were lower compared to hybrid treatment. Support, Table 3, Column 6, Table 4, Column 3. Contribution level: Overall average contributions dropped to 22 compared with 30.5 in the hybrid treatment. Actions above the Nash level of zero contributions amount 72.5 percent of data which is significantly lower than in hybrid treatment. Exact Nash level of zero contribution has been observed in 27.5 percent of data while hybrid treatment had only 9 percent. With no uncertainty still 19 percent of actions fall into level of fifty tokens. Fifty three percent of all actions were within the low range of contribution, [0, 25]. However, 32 percent of actions were above forty tokens. Surplus: The maximum surplus available had been achieved in 3 out of 130 periods. The mean surplus across groups was 289 and it was different from Nash prediction, 200 surplus, which was recorded in only four periods. Efficiency: The average efficiency reached 72 percent, while classical theory predicts 50 percent from maximum rent and it is below the efficiency reached in hybrid treatment (Wilxocon-Mann-Whitney test p=0.0337). There was a drop in cooperation level in standard treatment. The mean contributions and efficiency in period 1 were strongly significantly higher than aver- 14

15 ages in periods 5 and 10 (Wilcoxon rank-sum test p= and p=0.0019, correspondingly). Therefore, with no uncertainty in the individual exchange self-regarding subjects no longer prefer public account. Hence, contributions drop toward the end of game. Even though 31 percent of endowment remains in the public account because other-regarding subjects facing the risk to be ripped off by others, minimize regret by benefiting others in the group. 4.3 Shared Random Exchange We compare results in the shared random exchange with the standard treatment results. Result 3 Experimental results confirm low level of cooperation when public account has uncertain elements. Uncertainty in random treatment reduces contributions close to the average levels in the standard treatment. On average efficiency in random treatment were below than efficiency obtained in all other treatments. Support, Table 3 and 4, Column 4 Contribution: Exactly 24 percent of all actions confirm to the Nash equilibrium prediction of c i = 0 for some i. Overall, forty four percent of all actions were below 25 and above zero. However, only 22.5 percent of actions were above the 40 tokens. Actions in the range of [26;49] counts 18 percent of data. In total 14 percent of all actions are c i = 50. Mean individual contributions and total contributions were no different in the standard and random treatments. Efficiency: Overall rent reached 64 percent while predicted Nash level is 50 percent. Efficiency varies across groups from minimum of 44 to maximum at 88 percent. Wilcoxon rank-sum test shows highly significantly different averages across treatments. Efficiency and surplus were higher in the shared random treatment than in the standard treatment (p=0.0051). Also average efficiency was strongly higher in period 5 than in period 1 (p=0.1480) and mean efficiency was weakly higher in period 5 than efficiency in period 10 (p=0.0954). In line with prediction, free riders (low groupness) prefer the individual exchange and avoid uncertainty while cooperators (high groupness) tend to 15

16 contribute to the public account because they intrinsically value the public good that has now more risky nature than the standard treatment. Hence, in the shared random treatment the overall contribution level is low compared to hybrid treatment, however it remains constant throughout ten rounds. 4.4 Shared Maximum exchange Result 4 As predicted with incentives and the selection of maximum among investments, the efficiency increases and contributions were higher than in the standard treatment. Support, Table 3 and 4, Column 5 Contribution level: The average contribution level across groups was 16 tokens (32 percent of social optimal) with minimum at 9 and maximum at percent of population have chosen private account while another 29 percent decided to drop their initial level to zero contributions. This was due the fact that public account provided highest output only with one subject s willingness to contribute entire endowment. Here contributions were weakly significantly lower than in the standard treatment (p=0.0858). However, efficiency was highest among all four treatments given that 13 percent of subjects acted as a strong cooperators, c i = 50. As a result cooperation was at high level. There was continuous adjustment of multiple contributions into single one across periods. Thus, contributions in the 1st period were weakly higher than contributions in period 5, farther dropping to lowest value when reached period 10. Efficiency: With shared maximum exchange efficiency ranged from minimum of 69 to maximum of 99. The mean across eight sessions was 85 compared to prediction of 72. Due to the group account nature in shared maximum exchange efficiency reached high level even the contribution level was lowest among treatments. Efficiency and surplus were significantly higher in the shared maximum treatment than those values in the standard treatment (p= and p=0.0000). Also average efficiency were significantly higher than averages in hybrid treatment (p=0.0060). Efficiency stayed at the same level across periods and there was no ending effect. 16

17 4.5 Classification of behavioral types Public good experiments by Kurzban and Houser (2005) classify 20 percent of population to be a free-riders, 13 percent-cooperators and 63 percent being reciprocators. Croson (2007) finds reciprocity to be the dominant behavioral pattern in repeated VCM games where 71 percent of subjects contributed based on the actual median contribution of others. In Fischbacher et al. (2001) experiments with strategy method used for the elicitation of individual preferences, 50 percent of population were conditional cooperators (reciprocators), 33 percent were free-riders, and 14 percent exhibited hump-shaped patterns. We follow the same definition to identify reciprocal players and use positive Spearman correlation test between own contribution and the actual average of other s contributions as an indicator for reciprocal behavior. Table 6 depicts the composition of types for each treatment. Percent of conditional cooperators was highest, 77, in the standard treatment and was lowest in the hybrid treatment, 39. In the hybrid treatment 39 percent of subjects have positive Spearman coefficient (reciprocate others), 44 percent exhibit altruism and 15.4 percent fully cooperate irrespective of others decisions. In the standard treatment percent of recirpocators increases to 77 percent, percent of altruistic behavior drops to 15.4 percent, and percent of unconditional cooperators fell to 3.8 percent. In the shared random treatment 54 percent of subjects had significant positive Spearman coefficient (reciprocators). Percent of cooperators was 32.7, and 11.5 percent free ride. Composition of types changes to 56 percent of reciprocators, 12 percent of altruists, 23 percent of free riders and 9 percent of unconditional cooperators. Note that percent of reciprocators in the standard treatment is higher than other treatments: (i) in the hybrid treatment majority of subjects (44 percent with negative Spearman coefficient plus 15.4 percent of full cooperators) prefer public account; (ii) uncertainty in the random treatment discourages any cooperation and reciprocation; (iii) shared maximum exchange also discourages multiple full contributions into public exchange. In order to obtain maximum surplus here one subject has to be singled out for full contribution while others enjoy the benefit from public account in addition to private savings. We ran regression where dependent variable is individual s contribution. Independent variables are the actual average contribution of three others in the group in the same period, the period number, dummies for each group, dummies on individuals. The intercept in all regressions yields positive co- 17

18 efficient. In the standard treatment the coefficient on others contribution is positive and significant which tells us that subjects condition their contributions on others behavior. Note that in the hybrid treatment the coefficient on others contribution is negative and significant indicating the presence of altruism. However, we know that uncertainty in private account shift selfish players preferences into public account. In both shared random and shared maximum treatments coefficient on others average is positive, however it is not anymore significant. In all treatments period variable has negative sign suggesting that contributions dropped toward the end. 5 Discussion Altruism, inequity aversion, reciprocity, conformism, ostracism, risk and ambiguity are the alternative explanations of cooperative behavior that is not predicted by pure strategy Nash equilibrium in public good environment. We test endogenous preference change in VCM by introducing uncertainty aversion. In particular, hybrid condition with uncertainty in private account, shared random condition with uncertainty in public account, and shared maximum condition with incentive scheme compared to the standard public good condition. In all designs behavior is compared to point predictions for the symmetric Nash equilibrium and the social optimal outcome. Our results do confirm previous finding that at early periods of play subjects contribute percent of their endowment. In hybrid and standard treatments mean contributions in the first round were 64 percent of endowment while in the shared random and shared maximum treatments average contributions were 46 percent. We observed no sharp decline in contribution levels with ten periods of play in hybrid and shared random treatments. Thus, in the final stage subjects still contribute on average 51 percent of endowment to the public project in hybrid case and 39 in shared random treatment. In the standard and shared maximum treatments there was a decline in contributions over time, yet for the opposite motives. In the standard treatment cooperation was dropping with lower contributions while in the shared maximum treatment efficiency sustained at higher level (78 percent) as contributions lowered because a single person became a contributor for the sake of the group. Average efficiency was lowest (64 percent)in the shared random condition due to increased uncertain nature of public exchange. In the shared maximum and hybrid treatments average efficiency achieved high levels. We observed 18

19 highest cooperation in the shared maximum condition in terms of average efficiency (86 percent). In this treatment, most interestingly participants were able to coordinate their decisions, understand each other and absorb surplus close to the maximum available. This was available in the presence of unconditional cooperator (altruist) willing to contribute entire endowment to the public account having disadvantageous position in terms of relative payoff while others devote their endowment into private account and benefit from public account. In terms of dynamics subjects built up understanding and cooperation due to uncertain outcome in the private account in the hybrid condition. This cooperative behavior broke down in the consequent ten periods of standard public good condition with decline toward the end. However, decline was not very sharp; contributions remain at 33 percent and efficiency at 66 percent. In line with early experiments we have little spike at the beginning of the standard treatment since the second 10 periods were not announced ahead. There was no attempt to adopt previous cooperation in the standard treatment which tells us that subjects were responding more to incentives rather to group norms. As predicted shared random treatment had lowest level of efficiency and it remains low throughout ten periods. In the next ten periods of shared maximum treatment cooperation increases dramatically and sustains with little ending effect (e.g no drop in contributions). Here again subjects were responsive to incentives rather blindly following non-cooperative strategies obtained in early ten rounds. Again there was spike at the beginning of new (shared maximum) treatment related with the surprise new treatment. There was no difference recorded between reverse and regular designs in design 1. Wilcoxon signs rank test shows that period average contributions in hybrid treatments were higher than in the standard treatment in both reverse and regular designs (p= and p= respectively). Differing from, with regular design average contributions were higher in the shared random treatment than in the shared maximum treatment (p=0.0093), while in reverse design averages were no different from each other (p=0.1849). However, efficiency in the shared maximum was highest. 19

20 6 Further research This research has several extensions. With availability of several communities with public and private projects the results may differ. Next various institutions such as punishment or rewards can be explored. We may add voting into the model such that NE can be sustained by majority voting. We may relax assumption of exogenous exchanges such that community chooses whether they want to have a public account and see how the exchanges evolved change when people decide on the preferred project (public or private). Also, assumption of fixed population can be relaxed. We may add pre-treatment survey to identify grid/group attributes. 7 Appendix A Suppose there are only two actions available: contribute (c) entire endowment or not contribute (n). There are two states of nature: individual exchange turns into modified version of group exchange where return per capita is 1/4 or individual exchange stays as it is where return per capita is 1. Recall that the marginal per capita return from the public exchange is 1/2. Let the probability of occurrence for each states be p 1 andp 2 correspondingly. In the first case assume that individual is selfish and his/her utility does not incorporate the welfare of others in the group. Let assume that all others in the group have chosen to contribute. Then four outcomes are possible: (i) individual exchange become a modified group exchange and all contribute and everyone earns u c,1 = 1/2 4 e = 2 e where first subscript refers to the action and the second subscript indicates the state of the world; (ii) individual exchange stays as it is and individual under the consideration contributes to the public exchange. Then individual earns u c,2 = 2 e; (iii) individual exchange become a modified group exchange; individual free rides and earns u n,1 = 1/4 e + 1/2 3 e = 1.75 e; (iv) individual exchange stays as it is with return per capita equal to 1; individual free rides and earns u n,2 = e + 1/2 3 3 = 2.5e. Suppose p 1 = p 2 = 1/2. Expected regret of contributing to the public exchange expressed in the formula: d(c) = p 1 (max(u c,1, u n,1 ) u c,1 ) + p 2 (max(u c,2, u n,2 ) u c,2 ) (23) d(c) = p 1 (2e 2e) + p 2 (2.5e 2e) = p 2 0.5e = 12/ 0.5e > 0 (24) 20

21 Expected regret from not contributing is equal to: d(n) = p 1 (max(u c,1, u n,1 ) u n,1 ) + p 2 (max(u c,2, u n,2 ) u n,2 ) (25) d(n) = p 1 (2e 1.75e) + p 2 (2.5e 2.5e) = p e = 1/2 0.25e > (26) 0 Since d(c) > d(n) = 0 for the selfish player it is optimal not contribute to the project if p 2 0.5e > p e. Therefore, self-centered person will not contribute as long as probability of hybrid exchange staying as individual exchange is high enough, p 2 > 0.5 p 1. Now we examine the person who does care about of well-being of others in the group. The altruist person s utility function carries the payoff function of others in the group. Suppose Π i is the sum of the other s payoffs, then altruists utility function in each state of the world is given by: u i = π i + γπ i, where coefficient 1 < γ < 1 represents how much a person values other s welfare. For the altruist person γ > 0 and for the self-interested person γ = 0. For simplicity we assume the same coefficient applies for every other person in the group while individual may have different weights for other individuals in the group. Π c,1 = 2e3 = 6e; (27) Π c,2 = 6e; (28) Π n,1 = 1/2 3e 3 = 4.5e; (29) Π n,2 = 3e. (30) For the simplicity let γ = 1/2. Then individual utility for each combination of action and state is determined by: u c,1 = 2e + 6e (1/2) = 5e; (31) u c,2 = 0.5e + 6e (1/2) = 5e; (32) u n,1 = 1.75e + 1/2 3e 3 = 1.75e + 4.5e (1/2) = 5e; (33) u n,2 = 2.5e + +1/2 3e 3 = 2.5e + 4.5e (1/2) = 4.75e. (34) Expected regret of contributing is given by: d(c) = p 1 (max(u c,1, u n,1 ) u c,1 ) + p 2 (max(u c,2, u n,2 ) u c,2 ) (35) d(c) = p 1 (5e 5e) + p 2 (5e 5e) = 0 (36) 21

22 Expected regret from not contributing is equal to: d(n) = p 1 (max(u c,1, u n,1 ) u n,1 ) + p 2 (max(u c,2, u n,2 ) u n,2 ) (37) d(n) = p 1 (5e 5e) + p 2 (5e 4.75e) > 0 (38) Therefore, for the altruist person expected regret of contributing is lower than the expected regret of not contributing, 0 = d(c) < d(n). Hence this individual will maximize utility by contributing to the public project. Similarly, we can derive results for the case when all others in the group do not contribute. In that case for the selfish person utilities for each possible outcome are: u c,1 = 0.5e; (39) u c,2 = 0.5e; (40) u n,1 = 0.25e; (41) u n,2 = e. (42) Expected regret of contributing to the public exchange are given by d(c) = p 1 (max(u c,1, u n,1 ) u c,1 ) + p 2 (max(u c,2, u n,2 ) u c,2 ) (43) d(c) = p 1 (0.5e 0.5e) + p 2 (e 0.5e) = 1/2 0.5e = 1/4 e > 0 (44) Expected regret from not contributing is equal to: d(n) = p 1 (max(u c,1, u n,1 ) u n,1 ) + p 2 (max(u c,2, u n,2 ) u n,2 ) (45) d(n) = p 1 (0.5e 0.25e) + p 2 (e e) = 1/2 0.25e = 1/8 e > 0 (46) Since d(c) d(n), selfish subjects best choice fall to not contribute. Different story is in place with altruist person and his utilities for all possible outcome incorporate others payoffs as follows: u c,1 = 0.5e + γ(e e)3 = 2.75e; (47) u c,2 = 0.5e + γ(e e)3 = 2.75e; (48) u n,1 = 0.25e + γ(0.25e 3) = 0.625e; (49) u n,2 = e + γ(3e) = 2.5e. (50) Here γ is the group attribute that measures how much a person value well being of members in the group. Expected regrets of contributing or not contributing to the public exchange are given by: d(c) = p 1 (2.75e 2.75e) + p 2 (2.75e 2.75e) = 0 (51) d(n) = p 1 (2.75e 0.625e) + p 2 (2.75e 2.5e) = 1.19e > 0 (52) 22

23 Since contributing decision will make individual better off by minimizing expected regret, a person who has a high group measure, (γ), will contribute to the group project. 8 Appendix B Suppose there are only two actions available: contribute (c) entire endowment or not contribute (n). Assume only two states of the nature regarding others actions: all others contribute or all others do not contribute. Let the probability of occurrence for each states is p 1 andp 2 Also assume that individual is selfish and his/her utility does not incorporate the welfare of others in the group. In this case utility and payoff function are coincide. Then four outcomes are possible: (i) all contribute and everyone earns u c,1 = π c,1 = 1/2 4 e = 2 e where first subscript refers to the action and the second subscript indicates the state of the world; (ii) individual contributes while others do not contribute and individual earns u c,2 = 1/2 e == 0.5 e; (iii) individual free rides and others contribute such that earning are as follows u n,1 = e + 1/2 3 e = 2.5 e; (iv) everyone free rides and earns u n,2 = e. Expected regret of contributing to the public project expressed in the formula: d(c) = p 1 (max(u c,1, u n,1 ) u c,1 ) + p 2 (max(u c,2, u n,2 ) u c,2 ) (53) d(c) = p 1 (2.5e 2e) + p 2 (e 0.5e) = p 1 0.5e + p 2 0.5e = 1 > 0(54) Expected regret from not contributing is equal to: d(n) = p 1 (max(u c,1, u n,1 ) u n,1 ) + p 2 (max(u c,2, u n,2 ) u n,2 ) (55) d(n) = p 1 (2.5e 2.5e) + p 2 (e e) = 0 (56) Since d(c) > d(n) = 0 for the selfish player it is optimal to not contribute to the project. Now let see what happens if the person does care about of wellbeing of others in the group. Then altruist person s utility function carries the payoff function of others in the group. Suppose Π i is the sum of the other s payoffs, then altruists utility function in each state of the world is given by: u i = π i + γπ i, where coefficient 1 < γ < 1 represents how much a person values other s welfare. For the altruist person γ > 0 and for the selfinterested person γ = 0. For simplicity we assume the same coefficient for 23

24 every other person in the group while individual may have different weighing for each other individual in the group. Π c,1 = 2e3 = 6e; (57) Π c,2 = (e + 0.5e)3 = 4.5e; (58) Π n,1 = 1/2 3e 3 = 4.5e; (59) Π n,2 = 3e. (60) For the simplicity let γ = 1/2. Then individual utility for each combination of action and state is determined by: Expected regret of contributing is given by: u c,1 = 2e + 6e (1/2) = 5e; (61) u c,2 = 0.5e + 4.5e (1/2) = 2.75e; (62) u n,1 = 2.5e + 4.5e (1/2) = 4.75e; (63) u n,2 = e + 3e (1/2) = 2.5e. (64) d(c) = p 1 (max(u c,1, u n,1 ) u c,1 ) + p 2 (max(u c,2, u n,2 ) u c,2 ) (65) d(c) = p 1 (5e 5e) + p 2 (2.75e 2.75e) = 0 (66) Expected regret from not contributing is equal to: d(n) = p 1 (max(u c,1, u n,1 ) u n,1 ) + p 2 (max(u c,2, u n,2 ) u n,2 ) (67) d(n) = p 1 (5e 4.75e) + p 2 (2.75e 2.5e) > 0 (68) Therefore, for the altruist person expected regret of contributing is lower than the expected regret of not contributing, 0 = d(c) < d(n). Hence this individual will maximize utility by contributing to the public project. 9 Appendix C Suppose there are only two actions available: contribute (c) entire endowment or not contribute (n). Assume only two states of the world regarding others actions: all others contribute or all others do not contribute. Let 24