Conditional Cooperation in Network Public Goods Experiments

Transcription

1 Conditional Cooperation in Network Public Goods Experiments Luke A. Boosey a a Department of Economics, Florida State University, 288 Bellamy Building, Tallahassee FL, , USA. Abstract This paper examines experimentally the pattern of contribution decisions by heterogeneous groups in a network public goods game played on a circle. Stable contributions by unconditional behavioral types spread contagiously across the network, largely due to the presence of conditional cooperators. Free rider types appear to have a stronger influence than unconditional full contributors, consistent with the argument that conditional cooperation typically exhibits a downward or self-serving bias. JEL Classification: C9 D03 D83 H41 Keywords: contagion Network public goods game, voluntary contributions, conditional cooperation, 1. Introduction Many studies on the linear public goods game have demonstrated that a substantial fraction of individuals are conditional cooperators who contribute more when they expect others to do the same (see, e.g., Keser and Van Winden (2000), Fischbacher et al. (2001), Brandts and Schram (2001), Croson et al. (2005), Croson (2007), Fischbacher and Gächter (2010), Kocher et al. (2008)). Moreover, the result is often coupled with the claim that conditional cooperators exhibit a self-serving bias, and thus only attempt to partially match the increased contributions they expect from others (Fischbacher et al. (2001), Fischbacher and Gächter (2010), and Ambrus and Pathak (2011)). 1 There is also a growing literature on the importance of network structure for the decisions of agents whose interactions are governed by an underlying network. 2 In this paper, we examine the phenomenon of conditional cooperation in a network public goods game (NPGG) where each player s payoff depends only on his own contribution and the contributions of his immediate neighbors in I would particularly like to thank John Ledyard for providing financial support and detailed advice on this research. I am also very grateful to Jim Andreoni, Mark Isaac, Sebastian Goerg, Jean-Laurent Rosenthal, Leeat Yariv, Federico Echenique, Salvatore Nunnari, and Cary Frydman for their comments and suggestions on previous working paper versions of this manuscript. Special thanks also go to Chris Crabbe for programming the experiment in Multistage. addresses: lboosey@fsu.edu (Luke A. Boosey ), lboosey@fsu.edu (Luke A. Boosey ) 1 For a discussion of the literature, see the surveys by Ledyard (1995) and Chaudhuri (2011). 2 These include a comprehensive treatment by Galeotti et al. (2010), and several more targeted studies such as Bramoullé and Kranton (2007), Fatas et al. (2010), Rand et al. (2011), Carpenter et al. (2012), Boosey and Isaac (2014), Charness et al. (2014), and Leibbrandt et al. (2015). Preprint submitted to Journal March 14, 2015

2 the network. This game provides a particularly interesting environment for examining the importance of conditional cooperation and the composition of contribution types in groups. We report experimental fndings on the contagion of cooperation and free-riding when players are connected in a circle network. We find considerable heterogeneity in the behavioral types of players in the NPGG. Furthermore, in groups with a single free-rider (and no unconditional full contributors), the process of decay among conditional cooperators is faster, but still spreads gradually across the network. On the other hand, even in groups without any free-riders, an unconditional full contributor is only able to prevent (and in some cases only delay) the decline in contributions, rather than induce higher contributions. Thus, in addition to the composition of types in the group, the configuration of types, and especially the proximity of a conditional cooperator to an unconditional type, has an important effect on the pattern of contributions in network environments. 2. Experimental Design & Procedures The network public goods game (NPGG) is a natural extension of the standard linear public goods game with voluntary contributions. There are n players, each with an endowment of 100 tokens that may be allocated between a public good and private consumption. Public good consumption for a given player is determined only by the total level of contributions in his neighborhood. 3 Each game consists of 6 players connected within a circle network. Thus, player i s payoff is given by π i = 100 g i + A g i + (1) j N i g j where g j is player j s public good contribution, A is the marginal per capita return (MPCR) to the public good, and N i is the set of player i s direct neighbors in the network. In every game, the MPCR was set to A = 0.4, which induces the classical social dilemma, since each individual s incentive to free ride conflicts with the socially efficient outcome where everyone contributes their full endowment. The experiment consisted of 6 sessions with a total of 72 subjects at the Social Science Experimental Laboratory (SSEL) at the California Institute of Technology (Caltech). The experiment was programmed using the open source software, Multistage. Each session lasted approximately 1 hour and subjects earned on average US$25. Subjects participated in 4 independent matches, each consisting of 15 periods of the network public goods game in fixed groups. In each match, after every period, each subject was shown their own contribution decision, the total contributions made in their neighborhood, and their own payoff from the previous period. In addition, we varied the feedback provided to subjects about the decisions made by other players in their group. Specifically, in each match, subjects were shown one of four treatment conditions; the average contribution in their neighborhood (C-N ); the average contribution in the whole group (C-G); the average payoff in their neighborhood (P-N ); or the average payoff in the 3 This feature is based on the model introduced by Bramoullé and Kranton (2007), who propose the example of investment in innovation within a network. 2

3 Average Contribution Period P N P G C N C G Figure 1. Average contribution by treatment whole group (P-G). 4 In any given match, the feedback treatment condition was kept fixed across all 15 periods and all subjects observed the same treatment condition. The main findings discussed in the next section are consistent across treatment conditions. 5 Thus, in most cases, we pool the data from all four treatment conditions. 3. Results First, Figure 1 shows that at the aggregate level, average contributions exhibit the familiar pattern of decay with repeated play. Although the average appears to be slightly lower in the payoff conditions than the contribution conditions, the differences are not significant. At the individual-level, we first classify each subject as one of three key behavioral types in each match, based on their decisions in the match. Previous work by Fischbacher et al. (2001) (and several subsequent studies) use a variant of the strategy-method to elicit cooperative types, while Kurzban and Houser (2005) apply a statistical method to classifying subjects decisions. 6 We combine aspects of these two approaches, such that a subject in a particular match is classified as 4 Note that the C-N treatment condition is always implicity available to the subjects, since it can be deduced from total contributions in their neighborhood. 5 The rationale for introducing the different treatment conditions was to establish whether the feedback influences the summary statistic upon which conditional cooperators condition their contributions. Since this question is not our main focus in the present paper, we do not elaborate on the analysis of different treatments. 6 See also the classification of types by first-period contributions only in Gunnthorsdottir et al. (2007). 3

4 Table 1. Subject Classifications Treatment Classification P-N P-G C-N C-G Unconditional Full Contributors (U) Free-Riders (F) Conditional Cooperators (C) Other Total a free-rider (F) if in all but one of the first 14 periods 7 the subject contributed 10 tokens or less; an unconditional full-contributor (U) if in all but one of the first 14 periods, the subject contributed 90 tokens or more; a conditional cooperator (C) if the Spearman rank correlation coefficient between the player s contribution and the lagged average contribution in their neighborhood exceeds the critical value for a sample size of 14 in a one-sided test with p = 0.05; an other (O) contributor, if the subject did not satisfy the criteria for any of the other three classifications. The resulting classifications are summarized in Table 1. Consistent with previous studies, the classification procedure identifies a significant amount of conditional cooperation (between 39% & 57% in the treatments, 47% overall) and several unconditional free-rider types. In addition, apart from the P-G treatment, around 20% of the players are classified as unconditional full contributors. Next, we examine the influence of neighbors decisions on the conditional cooperators and other contributors. Figure 2 plots the average contribution over time for (C) and (O) types, broken down by the classifications of their two direct neighbors. Those with one (F) neighbor and one (C) or (O) neighbor converge much faster towards free-riding behavior themselves. In contrast, those who are neighbors with one (U) and one (C) or (O) exhibit almost no decay until the very last couple of periods. To check for these differences, we run a simple panel regression on contributions against an interaction term between period and neighbors classifications. Wald tests for differences between coefficients indicate significantly larger slope coefficients for (F-C) and (F-O) players than for (U-C) or (U-O) players, and while the slopes are the same for (F-C), (F-O), and (C-C) players, there is a significant level effect on the latter relative to the two former. Importantly, unconditional full contributors do not induce their conditional cooperator neighbors to converge towards full contributions. This lends further support to previous findings that suggest conditional cooperation exhibits a downward or self-serving bias. 8 7 We discard the final period from each match to eliminate endgame effects and introduce a tolerance for a deviation 4

5 Average Contribution Unconditional Full Contributors (U) Free Riders (F) (U C) (U O) (C O) (O O) (C C) (F C) (F O) Period Figure 2. Average Contributions over time for Conditional Cooperators based on their immediate neighbors classifications Nevertheless, Figure 2 only tells part of the story in the network environment, since the composition of players in the rest of the group may also be critical. Recent studies by de Oliveira et al. (2015), Chaudhuri and Paichayontvijit (2006), and Fischbacher and Gächter (2010) have addressed the importance of group composition in the standard linear VCM game. Our findings for the network setup reinforce the result obtained in de Oliveira et al. (2015) (for the standard environment) that group composition has both first and second-order effects on cooperation levels. The second-order effects capture the impact of unconditional types on the decisions made by conditional cooperators. 9 In particular, consider groups with a single free-rider (F) type and five conditional cooperators (C) or other contributors (O). Here, conditional cooperation would not only suggest that contributions decay over time, it would also imply different rates of decay for players located closer to or further from the free-rider in the network. Figure 3 illustrates that this pattern emerges for the groups with a single free-rider in our experiments. There were 10 such groups across the four treatments. Figure 3 shows the average contribution in the first period and in each 4-period block from period 3 to 14, for the free-rider, for the two players who are direct neighbors of the free-rider (F + 1), the two players who are two steps from the free-rider (F + 2), and the player who is from the presecribed behavior in one period. 8 For example, see Fischbacher et al. (2001), Fischbacher and Gächter (2010), Ambrus and Pathak (2011) and de Oliveira et al. (2015). 9 Note that in de Oliveira et al. (2015), the focus is only on the free-riders influence on conditional cooperators, and does not address the impact of unconditional full contributor types. 5

6 Figure 3. Average contributions in groups with 1 free-rider. F indicates the free-rider; F + 1 denotes the two players located one step from the free-rider; F +2 denotes the two players who are two steps from the free-rider; F + 3 denotes the player located three steps from the free-rider. Figure 4. Average contributions in groups with 1 or 2 unconditional full contributors. U indicates the unconditional full contributor; U + 1 denotes the two players located one step from a U; U + 2 denotes the two players who are two steps from a U; and U + 3 denotes the player located three steps from a U (when applicable). three steps from the free-rider (F + 3). Furthermore, using the first 7 periods of data, the slope coefficients on period in a simple OLS regression on contributions are 4.34 (p = 0.000) for (F + 1), 2.58 (p = 0.038) for (F + 2), and 1.26 (p = 0.491) for (F + 3), which suggests earlier and significantly faster decay by players closer to the free-rider. Using the last 7 periods (excluding the last period), these coefficients are 4.08 (F + 1), 3.22 (F + 2), and 2.91 (p = 0.000) for (F + 3). In Figure 4, we show the average contribution by player proximity to the (U) player over the same period blocks, using groups with 1 (U) player, as well as groups with 2 neighboring (U) players. 10 Notably, the full contributors are not able to induce convergence towards full cooperation. In fact, players who are three steps from the full contributor exhibit significant decay. However, players closer to the unconditional full contributor increase contributions at first, and display considerably weaker tendency to decay over time. Comparing the slope coefficients on period in an OLS regression using the first 7 periods, we find a significant, positive slope for (U + 1), statistically insignificant (positive) slope for (U + 2), and a large, significant negative slope for (U + 3). Using the last 7 periods, we get slightly negative (but statisticaly insignificant) slope coefficients for (U + 1) and (U + 2), and a significant negative coefficient (though weaker than in the first 7 periods) for (U + 3). Altogether, the results for these two kinds of groups confirm that the impacts of unconditional types on conditional cooperators depend strongly on proximity There are 4 groups with a single (U) and 4 groups with two (U)s located next to each other. 11 Although we do not report or discuss them here, other group compositions, where both unconditional types are present (or where neither are present), also exhibit the gradual process of decay, consistent with the hypothesis of imperfect or partial conditional cooperation. The precise contribution patterns in these kinds of groups warrant further research. 6

7 4. Conclusion The findings reported in this paper illustrate that the mechanics of conditional cooperation can be particularly salient in network public goods games. Players who always contribute almost everything (unconditional full contributors), and players who always contribute very little (freeriders) can either speed up or delay the breakdown of cooperation. Importantly, as has been suggested for the standard linear public goods environment, there appears to be a downward or self-serving bias to conditional cooperation, such that even in groups with a full contributor and without a pure free-rider type, the players do not converge to full cooperation. In addition, the influence of the unconditional types is perhaps understated, since players in these experiments only observe the average contribution in their neighborhood. Nevertheless, the evidence of contagion in the circle NPGG environment studied here is encouraging for future research into the effects of other network structures on contribution decisions, particularly as they relate to the various theories of social preferences, reciprocity, and learning behavior that have been advanced to explain conditional cooperation. References Ambrus, A. and P. A. Pathak (2011). Cooperation over finite horizons: a theory and experiments. Journal of Public Economics 95 (7), Boosey, L. and R. M. Isaac (2014, December). Network monitoring and punishment in public goods experiments. Working Papers wp , Department of Economics, Florida State University. Bramoullé, Y. and R. Kranton (2007). Public goods in networks. Journal of Economic Theory 135 (1), Brandts, J. and A. Schram (2001). Cooperation and noise in public goods experiments: applying the contribution function approach. Journal of Public Economics 79 (2), Carpenter, J., S. Kariv, and A. Schotter (2012). Network architecture, cooperation and punishment in public good experiments. Review of Economic Design 16 (2-3), Charness, G., F. Feri, M. A. Meléndez-Jiménez, and M. Sutter (2014). Experimental games on networks: Underpinnings of behavior and equilibrium selection. Econometrica 82 (5), Chaudhuri, A. (2011). Sustaining cooperation in laboratory public goods experiments: a selective survey of the literature. Experimental Economics 14 (1), Chaudhuri, A. and T. Paichayontvijit (2006). Conditional cooperation and voluntary contributions to a public good. Economics Bulletin 3 (8), Croson, R., E. Fatas, and T. Neugebauer (2005). Reciprocity, matching and conditional cooperation in two public goods games. Economics Letters 87 (1), Croson, R. T. (2007). Theories of commitment, altruism and reciprocity: Evidence from linear public goods games. Economic Inquiry 45 (2), de Oliveira, A. C., R. T. Croson, and C. Eckel (2015). One bad apple? heterogeneity and information in public good provision. Experimental Economics 18 (1),

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