چه کسی در بازی های مکرر همکاری می کند: نقش نوع دوستی، بیزاری از نابرابری و جمعیت شناسی

We explore the extent to which altruism, as measured by giving in a dictator game (DG), accounts for play in a noisy version of the repeated prisoner's dilemma. We find that DG giving is correlated with cooperation in the repeated game when no cooperative equilibria exist, but not when cooperation is an equilibrium. Furthermore, none of the commonly observed strategies are better explained by inequity aversion or efficiency concerns than money maximization. Various survey questions provide additional evidence for the relative unimportance of social preferences. We conclude that cooperation in repeated games is primarily motivated by long-term payoff maximization and that even though some subjects may have other goals, this does not seem to be the key determinant of how play varies with the parameters of the repeated game. In particular, altruism does not seem to be a major source of the observed diversity of play.

Understanding when and why people cooperate in social dilemmas is a key issue not just for economics but for all of the social sciences (as noted by e.g., Ahn et al., 2003 and Gächter and Herrmann, 2009). Here we focus on the infinitely (i.e., indefinitely) repeated prisoner's dilemma, where cooperation can be an equilibrium if future payoffs loom sufficiently large compared to the present. Laboratory experiments have shown that the overall fraction of subjects who cooperate once they have some experience with the game depends on the payoff parameters, with cooperation being much more prevalent when the returns to cooperation are higher and the future looms larger (e.g., Dal Bó and Frechette, 2013 and Rand and Nowak, 2013). Nonetheless, there is typically some cooperation even when cooperation is not an equilibrium, and some defection when cooperative equilibria exist. Moreover, there is substantial heterogeneity across subjects in a given treatment: Some may cooperate in most periods while others cooperate hardly at all. This raises the question of who these cooperators are, if they differ in other measurable characteristics from the subjects who do not cooperate, and how such differences vary depending on the gains from cooperation. Understanding the heterogeneity of play seems useful for understanding when cooperation will arise, and also for the debate about the role of other-regarding or “social” preferences in supporting cooperation. In particular, the data raise the question of whether the cooperators are motivated by more than just maximizing their own monetary payoff. Although other-regarding motivations clearly play an important role in generating cooperative behavior in some interactions, the extent to which they affect play in infinitely repeated games remains largely unknown. As a first step toward understanding the sources of heterogeneous play and the way subjects respond to changes in game parameters, we combine data on play in an infinitely repeated noisy prisoner's dilemma or “RPD” that was previously analyzed in Fudenberg et al. (2012) with data from an additional dictator game played by the same subjects, and also with survey responses and demographic data.1 First, we relate each subject's play in the RPD to their generosity in a dictator game (DG). Next, we investigate whether accounting for inequity aversion (Fehr and Schmidt, 1999) or pure altruism does a better job of explaining the observed distribution of strategies than money maximization. In addition, we use responses to survey questions to explore the motivations underlying cooperative play in the RPD, as well as to explore whether self-reported prosocial behavior outside the laboratory is a good indicator of experimental behavior in the RPD and DG. We also examine whether individual characteristics such as age, major, gender and risk attitudes are useful in explaining heterogeneity. In the RPD, subjects could either cooperate or defect in each round, with a constant probability of continuing to another round, and a constant probability that each player's decision will be changed to the opposite. At the end of the last repeated game, subjects played a DG. To reduce the influence of RPD play on the DG, we specified that the recipient would be a subject in a later experiment; this was easy to do with the DG but would have been more difficult to implement with a sequential-move game such as the ultimatum or trust games. Behavior in the DG is known to be affected by factors such as double blindness, adding third players, random moves, or expanded choice sets (e.g., Hoffman et al., 1994, List, 2007, Bardsley, 2008 and Cooper and Kagel, forthcoming). Nonetheless, DG giving has been shown to correlate with charitable giving (e.g., Benz and Meier, 2008) and returning money mailed to subjects in misaddressed envelopes months or years after the DG (Franzen and Pointner, 2013), suggesting that the DG does provide relevant information about altruistic preferences. Moreover, the DG is not the only game where behavior is sensitive to strategically incidental factors: behavior in other games commonly used to measure social preferences, such as the ultimatum game, the one-shot prisoner's dilemma and related public goods games, can react to both priming and framing (e.g., Liberman et al., 2004, Leliveld et al., 2008, Benjamin et al., 2012, Ellingsen et al., 2012, Rand et al., 2013 and Rand and Engel, forthcoming); and, at least in Dreber et al. (2013), DG giving is less influenced by framing effects than the Prisoner's Dilemma. The returns to cooperation in the RPD varied, with four different payoff specifications. While the frequency of cooperation varied also with the payoff specification, giving in the DG did not, which suggests that spillovers from the RPD to the DG were minimal. When we predict RPD cooperation with DG play, we find that an individual's giving in the DG is not correlated with either playing C in the first period of the repeated game or the overall frequency of cooperation in the repeated game, except in the one “non-cooperative” treatment where cooperation is not an equilibrium. In addition, we find no correlation between DG giving and leniency (waiting for multiple defections before punishing) which is substantially more frequent when the returns to cooperation are high, and earns high payoff in these treatments; and we find no correlation between forgiveness (returning to cooperation after punishing) and DG giving, except in the non-cooperative treatment. We also relate DG giving to the distribution of strategies played, and find that players who are selfish in the DG are more likely to play “Always Defect” in the non-cooperative treatment, while selfish players are marginally significantly less likely to play always defect in the “cooperative” treatments where cooperation is an equilibrium. Thus altruism as measured by DG giving seems to play a role in promoting cooperation only when cooperation is not supported by self-interest. When the monetary payoffs strongly support cooperation, DG giving has little explanatory power, and what power it may have suggests that in these cases selfishness promotes rather than inhibits cooperation. We also explore the implications of one sort of social preferences for play in our RPD game through the use of the Fehr and Schmidt inequity aversion model (1999). While the FS model does not capture many important aspects of social preferences such as reciprocity, spite and efficiency concerns (e.g., Rabin, 1993, Levine, 1998, Brandts and Solà, 2001, Charness and Rabin, 2002 and Cox et al., 2008), and does not allow for a preference for ex-ante equality (e.g., Bolton et al., 2005, Krawczyk and Le Lec, 2010 and Fudenberg and Levine, 2012), it is a parsimonious and widely used specification that is easy to implement, readily yields concrete predictions, and provides a straightforward basis of comparison to monetary payoff maximization.2 To apply the FS model, we investigate the expected utility of the various strategies used in the experiment if subjects had utility as described by the inequity aversion model with parameters α = 2, β = 0.6, where α measures the loss from disadvantageous inequity and β measures the loss from advantageous inequity. We chose these parameters because Fehr and Schmidt (2010) argue that many experiments are well summarized by supposing that some fraction of the population has these payoffs and the rest has “standard” payoffs α = β = 0. With these parameters, the highest utility goes to subjects that always defect in the non-cooperative treatment, and to a very infrequently played exploitive or ‘suspicious’ strategy in the cooperative treatments. Since maximizing money payoff also predicts “always defect” in the non-cooperative treatment, allowing a fraction of the population to have the preference that the FS model suggests does not help explain why some subjects continue to cooperate here. And since the “suspicious” strategy was rarely played in the other treatments it is unlikely to have had much impact on play of other subjects. 3 Moreover, the FS model gives relatively little utility to lenient strategies, which are common in the cooperative treatments and earn large monetary payoffs. Thus allowing for some subset of the population to have FS preferences does not yield better predictions in the cooperative treatments either, especially since the main deviation in observed play from money maximization was an excess of players using the strategy always defect. We also examine a simple altruistic preference where subjects derive some benefit from their partner's payoff. We find that although altruism can potentially explain the cooperation we observe in the low payoff specification, it too makes incorrect predictions (in this case, an excess of cooperation) when the returns to cooperation are large. Third, we analyze subjects’ motivations for cooperating in the RPD. Subjects indicated how well various motivations (both self-interested and other-regarding) explain their cooperation decisions. We analyze the relationship between these motivations and cooperative play in the RPD. At the individual level, we find that across all payoff specifications, a large majority of subjects reported maximizing their long-term payoff as a more important motivator of playing cooperatively than either a desire to increase their partner's payoff, to do the morally right thing or to avoid upsetting their partner. At the aggregate level, we find that the desire to maximize payoff was a more consistent predictor of RPD cooperation than any of the other motivations. We also assess the role of subjects’ beliefs about the intentions of others, and find that subjects who are more inclined to attribute unprovoked defections to error are more cooperative, but that DG giving is not predictive of this tendency to give the opponent the benefit of the doubt. Fourth, we examine the correlation between behavior that is observed in the experiments and that is self-reported in survey questions related to the domains of benevolence and universalism. Answers to these survey questions have been previously related to both how spouses/partners and peers answer these questions on behalf of the subjects’ behaviors, as well as to benevolence and universalism values (Bardi and Schwartz, 2003). However, we find that these questions do not predict experimental behavior in the RPD, except for in the non-cooperative treatment where there is some evidence of a negative correlation between cooperation and these measures. There is, however, evidence of a positive correlation between DG giving and benevolence. Finally, we explore whether specific individual characteristics are correlated with experimental behavior. Both descriptive measures and the distribution of strategies played suggest that women are less cooperative than men, and provide some evidence that economics majors cooperate less than non-economics majors. We find no gender or major differences in DG giving. The other individual characteristics explored have no consistent relation to the various measures of cooperation. This suggests that individual characteristics may have some role, but perhaps not a very substantial one, in explaining heterogeneity in RPD play. As far as we know, this is the first paper that correlates behavior in the RPD and DG while also linking social psychology survey questions with behavior in both games. Harbaugh and Krause (2000) is perhaps the most related previous paper; they had subjects (children) first play a finitely repeated public goods game and then a modified DG, and they find that DG giving is correlated with first-round contributions but not last-round contributions, although their sample in this treatment is less than 30 subjects. Blanco et al. (2011) find no correlation between play in the DG and play in a one-shot public goods game (PGG) but do find a positive correlation between the DG and second-mover play in a sequential PD; it is not clear how to extrapolate from their results to the RPD. There are two recent studies that explore the role of social versus selfish reasons for cooperation in repeated games. Cabral et al. (2010) and Reuben and Suetens (2012) examine whether subjects are selfish by varying whether the subjects know the current round of an interaction is the last. Cabral et al. test for and reject a specific model of backwards-looking reciprocity; Reuben and Suetens classify subjects as selfish/reputation building, strong reciprocators, unconditional defectors or unconditional cooperators by also letting subjects condition on whether the opponent cooperated or defected. Both Cabral et al. and Reuben and Suetens conclude that the majority of subjects are selfish. These results are in line with what we find. Our use of survey questions is related to previous studies linking experimental behavior to survey questions, where the focus has been on the trust game and trust attitudes (e.g., Glaeser et al., 2000, Fehr et al., 2003 and Sapienza et al., 2013) or on cooperative play in one-shot cooperation games and trust attitudes (Ahn et al., 2003 and Gächter et al., 2004). The results thus far are mixed, with some papers finding that attitudinal trust questions are not good at predicting experimental behavior (Glaeser et al., 2000 and Ahn et al., 2003) whereas others find that they are (Fehr et al., 2003 and Gächter et al., 2004). In the setting of the DG, Carpenter et al. (2008) find that the specific survey questions for altruism used in their study are positively correlated with DG giving. There have been several past studies on the correlation of individual characteristic variables and cooperation. Economics majors have been found to cooperate significantly less in the one-shot (Frank et al., 1993 and Dal Bó, 2005) and fixed-length (Dal Bó, 2005) PD; in the RPD without execution errors, however, Dal Bó (2005) and Dreber et al. (2008) find that the effect goes in the opposite direction, with economics majors cooperating more. Evidence on the importance of gender for cooperation is mixed (surveyed in Croson and Gneezy, 2009), as is the role of socio-economic variables (e.g., Glaeser et al., 2000 find positive results in a trust game (TG), whereas Gächter et al. (2004) find no correlation with play in a one-shot PGG). A recent meta-analysis of the DG, however, found that women give more, and that older individuals give more than younger individuals (Engel, 2011).