قدرت کنوانسیون: نظریه ترجیحات اجتماعی

Abstract People often act as if they care about others’ welfare as well as their own (i.e. have “social preferences”). One plausible assumption is that people have preferences for social implications of their actions, determined by exogenous “conventions”, in addition to the material consequences of actions. I construct games with conventions using the psychological games framework developed in Geanakoplos et al. [Geanakoplos, J., Pearce, D., Stacchetti, E., 1989. Psychological games and sequential rationality. Games and Economic Behavior 1, 60–79]. With a notion of distributional convention combining efficiency and fairness, I show equilibrium behavior reflects social preferences. The model yields tight and testable predictions consistent with a large body of experimental results, is parsimonious, and is suggestive of further studies, both experimentally and theoretically.

Introduction Social preferences refer to the phenomena that people seem to care about certain “social” goals, such as the well-being of other individuals or a “fair” allocation among members in society, in addition to their own material benefits. The evidence is ample; Camerer, 2003 and Kahneman and Tversky, 2000 and Sobel (2005) all contain extensive accounts of both real life examples and experimental results. Depending on the fine details of the environment, social preferences exhibit many patterns: sometimes people reciprocate, rewarding kindness and punishing unkindness; sometimes people show unmotivated altruism; sometimes people act in the entire group’s interest, even if it hurts some individuals in the group. The following experimental results are illustrative of the variety of the patterns of social preferences. 1. In an experiment of the dictator game,1 subjects choose between pairs of (self, other) allocations. About 50 percent of the subjects choose (375, 750) over (400, 400) (Charness and Rabin, 2002). 2. Subjects first play a dictator game, choosing between (self, other) allocations of (US$ 10, US$ 10) and (US$ 18, US$ 2).2 Then some choices were randomly selected and realized. Finally, those subjects whose decisions were not realized were given the choice of evenly splitting US$ 12 with a person whose first offer was (18, 2) or evenly splitting US$ 10 with a person whose first offer was (10, 10). The one who was not chosen for the interaction receives 0. About 74 percent of the subjects chose the latter (Kahneman et al., 1986). 3. Two players sequentially make private contributions to a public good, which is supplied either at the maximum of the two contributions (the best-shot game) or at the sum of them (the summation game). The first-mover has a smaller marginal-willingness-to-pay than the second-mover.3 Subjects behave very differently in experiments of these two games: the first-mover typically does free ride in the best-shot game, but not in the summation game; in addition, when the first-mover contributes 0, the second-mover responds by contributing 0 almost three times more often in the summation game than in the best-shot game (Andreoni et al., 2002). 4. The ultimatum game is another famous example where theoretical prediction fails.4 In laboratory experiments, it is rarely observed that the proposer demands the entire sum, and offers of 20–30 percent are frequently rejected. Offers of 50/50 split are observed in all experiments, often being the mode. With stakes between US$ 5 and US$ 20 and as high as US$ 100, the average offer is around 40 percent of the sum. Moreover, the rejection rate seems to depend on possible offers the proposer did not make. For instance, when the proposer chooses between offering 20 or 75 percent, an offer of 20 percent is rejected 33 percent of the time; however, when the proposer’s choice set is changed to (20 percent, 87.5 percent), the rejection rate for an offer of 20 percent drops to 16 percent Brandts and Sola, 2001, Camerer and Thaler, 1995, Charness and Rabin, 2002 and Thaler, 1988. It turns out to be a challenging task to explain all these complex patterns in a parsimonious model. The existing literature on social preferences includes two main classes of models, the distributional preferences models and the reciprocal preferences models. Distributional preferences models assume players have preferences over final payoff allocations. For example, Fehr and Schmidt (1999) and Bolton and Ockenfels (2000) explain the ultimatum game results by assuming that players dislike inequality in final payoff allocations. However, these models cannot explain why players prefer an unequal payoff allocation to their own disadvantage as in Example 1. Altruism and social welfare models along the line of Andreoni (1990) and Andreoni and Miller (2002) assume players prefer a higher payoff for the opponents or the entire group of players in the game. These models can explain self-sacrificing behavior as in Examples 1 and 3, but cannot explain Pareto damaging behavior such as rejecting low offers in ultimatum games. In fact, Example 3 clearly indicates that players’ preferences over final payoff allocations alone cannot explain social preferences. When the first-mover contributes nothing, the set of payoff allocations the second-mover can generate is exactly the same in the two public-good games. Yet the second-mover makes systematically different choices. There must be something other than final payoff allocations that enters players’ considerations. In a seminal paper (Rabin, 1993), Rabin argues that it is reciprocity that makes the difference. Rabin assumes social preferences are driven by players’ kindness towards each other: if a player believes the opponent’s action is motivated by kindness toward him, he then prefers to react kindly, and vice versa. This model successfully accounts for retaliatory and altruistic behavior. Such reciprocal preferences models are intuitively appealing and further explored in Falk and Fischbacher (2006) and Dufwenberg and Kirchsteiger (2004), among others. Rabin offers a zero-parameter model. Players strictly prefer either the kindest action or the meanest action, depending on their beliefs about the opponent. Such pure reciprocity does not explain unmotivated altruistic behavior (Example 1), or why subjects would punish, at their own cost, somebody who is mean to another person (Example 2). In addition, the simple split-the-difference fairness notion often fails to capture the context of the game. For instance, according to this fairness function, in Example 4, offering 20 percent would be strictly fairer in the first game than in the second game, if the proposer can offer 0, but then there should be fewer rejections in the first game than in the second, inconsistent with the experimental results. One solution is to write the missing components into the utility function and adding parameters. In fact, in his appendix, Rabin suggests that to have unmotivated altruism in the model, one could add a parameter to capture the relative strength of such concerns in comparison to that of reciprocity.5 The unsatisfactory performance of the naive fairness function could be due to its lack of an objective criterion reflecting social concerns as suggested in the distributional preferences models. Charness and Rabin suggest a comprehensive model along this line. Their model uses six parameters to summarize how players weigh social preferences in their total preferences, how they weigh fairness in comparison to efficiency, and how they punish those opponents whom they believe to fail to be sufficiently concerned about other people according to some social standard. The model formalizes the most important heuristic patterns of social preferences observed in experiments. In particular, it combines distributional preferences with reciprocal preferences. The model fits important experimental results in the literature. However, with so many parameters, the model is rather unrestrictive in making interpretations and predictions, while at the same time it is too restrictive in that it does not allow for heterogeneity across players or any other forms of social preferences. In this paper, I explore an alternative perspective to social preferences. In each of the above examples, the players seem to share some normative standpoint of what each of them “ought to” do given what could be done. I refer to this normative standpoint as “the convention”. Players prefer to conform to the convention and prefer their opponents to conform to the convention as well. In the dictator game and the ultimatum game, it is conventional for the proposer to share the money with the opponent evenly. In the public-good game, it is conventional for players to contribute as long as they benefit from the public good and as long as their contributions count. Under common knowledge of these conventions, subjects are willing to give up some material benefits in order to conform to the convention (Experiment 1), to choose an opponent who conforms to the convention (Experiment 2 and the best-shot game in Experiment 3), and when having to interact with an opponent who has the opportunity to conform to the convention but chooses not to, to refuse to conform to the convention themselves (the summation game in Experiments 3 and 4). A notable departure of the above story from the distributional preferences models is that players do not care about others’ welfare per se. Rather, they only try to conform to conventions, which may incorporate some received notions about how the resources should be allocated among players. On the other hand, this explanation is also subtly different from reciprocal preferences models in that players do not care about the opponents’ intentions towards themselves; instead, they care about the opponents’ intentions towards the convention: how much the opponents conform to the convention compared to themselves. I assume players receive payoffs from the social implications of their actions according to the convention, and the payoffs come from two additively separable components: conformity effects, players prefer to conform to the convention, and interaction effects, players prefer their opponents to conform to the convention to a degree at least as much as themselves. The total payoffs are the weighted average of the material payoffs and such social payoffs. The weight is interpreted as the salience of the convention one perceives in a game, which can be heterogeneous across players. Intuitively, a convention induces a ranking over all possible actions in terms of their “appropriateness” or the degree of “right and wrong”. The higher an action is ranked, the more desirable it is in terms of its social implications. Whether an action is appropriate depends on what appears to be the relevant context, which in turn depends on the player’s feasible alternatives and beliefs about the opponent’s action. Therefore, I model conventions as rankings of all actions conditional on the player’s belief about the opponent’s action. Assuming common knowledge of the convention and payoffs, 6 using the psychological games framework developed in Geanakoplos et al. (1989) (henceforth GPS), I construct games incorporating conventions for two-person normal-form games. Conventions are exogenous in this model. They are part of the definition in the psychological game. In principle, conventions could reflect political ideal, religion, tradition and so on, and do not necessarily depend on payoffs. The same material game can be associated with different conventions, depending on the contexts of the game. In economic context, it seems the most relevant conventions are criteria regarding allocations of the payoffs. Thus, I am most interested in distributional convention, which is based on payoff allocations and reflects some social standard based on efficiency and fairness criteria. Social preferences emerge naturally in equilibrium of games with distributional convention. With only one parameter summarizing the (heterogeneous) attitude towards conventions across players and two parameters summarizing the distributional convention, the model generates tight predictions consistent with a large body of experimental results. The separation of conventions and players’ attitudes towards conventions makes it possible to isolate the effects of changes in conventions and heterogeneity across players on equilibrium behavior, which is suggestive for further experimental study. The general model could incorporate a wide range of social effects. In the class of games I am most interested in, namely games with distributional conventions, the model is comparable to Charness and Rabin, but with a more flexible structure, fewer parameters and heterogeneous players. The paper proceeds as follows. Section 2 presents the basic model. Section 3 focuses on models with distributional convention. Two examples are discussed at length: the symmetric two-by-two games (including the prisoner’s dilemma game, the pure coordination game and the chicken game) and the public-good games (including the summation game and the best-shot game). Section 4 concludes. Proofs not found in the text are collected in Appendix in Supplementary data.

Concluding remarks I propose a simple model to account for social preferences. The model takes “conventions” as given and hypothesizes that people prefer to conform to conventions and prefer the opponent to conform to conventions as well. Formalizing distributional convention as a belief-dependent ranking over the whole strategy space according to some combination of efficiency and fairness principles, I show that equilibrium behavior in games incorporating distributional convention reflects social preferences. For concrete examples, I show that the model makes sharp predictions in symmetric 2×22×2 games and public-good games that are consistent with experimental evidence. The simplicity and parsimony of the model make it particularly appealing empirically. The separation of heterogeneous salience of convention and the convention itself, and the fact that the convention parameters are obviously experimentally manipulatable make it easy to test the model empirically. For example, in symmetric 2×22×2 games, holding everything else constant, the model predicts that equilibrium outcome varies with the material payoff details, for example, a−ca−c; in particular, the model predicts distinctly different behavior when the material payoff structure is that of the chicken game. In the public-good game, the model predicts different sets of social equilibria in the two games for fixed salience parameters θ1,θ2θ1,θ2. Conceptually, the model also differs from the main body of the social preferences literature in that in a sense, inter-dependent utilities are not the primitives of the model. In this model, the presence and nature of inter-dependent utilities only reflect the presence and nature of exogenous conventions. In a social equilibrium, by taking into account the actions’ social implications, which are evaluated according to some convention that depends on overall payoff allocations, players act as if they care about each other. The nature and pattern of “social preferences” reflect the nature and pattern of the prevailing distributional convention in the game. By manipulating the distributional convention in a game, one could change the pattern and/or degree of such inter-dependence.28 The model embraces an “instrumental view” of conventions in one-shot games that is reminiscent of the repeated games or evolutionary arguments for social preferences. One can view a convention as a coordination device: it suggests an appropriate action (or actions) to each player in each and every context; given the strategic complementarity of the social payoffs, for sufficiently convention-conscientious players, a fixed point of the “social best response” correspondence is a social equilibrium, achieving the outcome the convention targets. Furthermore, the concept of conventions is reminiscent of notions such as social norms, ethics, morals and so on. The model connects social preferences to questions such as these: what social norms are sustainable in the long run? What determines the emergence and fading of particular moral principles? This suggests that a thorough understanding of social preferences must be based on a theory of evolution of social norms. There are a number of interesting extensions one can study. Multi-person games and dynamic games are the most obvious ones. How do people respond to an environment where multiple opponents take actions with different social implications? How do people draw inferences when such inferences affect their utilities directly in dynamic games? How to evaluate the social implications of an action in these complex environments? These are open questions that invite both experimental and theoretical examinations. The current model provides a framework that highlights the additional questions that need to be answered and sheds light on possible experimental design. In real life, people do not always share the same convention. For example, people from different cultural backgrounds may respect different ethical principles or attach different weights to even the same set of ethical principles; hence they evaluate an action’s social implications differently. One could imagine that a bargaining impasse could result from each bargainer evaluating the social implications of actions using the convention most favorable to his own material benefits. Such issues could be dealt with in a tractable way using the framework presented in this paper, for example, by introducing payoff uncertainties into games with multiple conventions.