ترجیحات اجتماعی ناهمگن

Abstract Recent research has shown the usefulness of social preferences in explaining behavior in laboratory experiments. This paper demonstrates that models of social preferences are particularly powerful in explaining behavior if they are embedded in a setting of heterogeneous actors with heterogeneous (social) preferences. For this purpose a simple model is introduced that combines the basic ideas of inequity aversion, social welfare preferences, reciprocity and heterogeneity. This model is applied to 43 games, and its predictive accuracy is clearly higher than that of the isolated approaches. Furthermore, it can explain most of the “anomalies” discussed in Goeree and Holt [Goeree, J., Holt, Ch.A., 2001. Ten little treasures of game theory and ten intuitive contradictions, American Economic Review 91, 1402–1422].

Introduction When we meet somebody for the first time we often ask ourselves what kind of person he or she is. This is not just a matter of pure curiosity; it is mostly the central question in deciding whether to have further contact with that person. Such a way of thinking suggests that people are indeed very different from each other and that the type of the person we are interacting with is of utmost importance. However, most models in economic theory and particularly in game theory assume homogeneous actors with identical preferences. Differences in behavior usually stem from different initial equipments and different positions in the game under consideration. The main purpose of this paper is to demonstrate the usefulness of explicitly modeling heterogeneity of preferences in explaining the behavior of subjects in 43 laboratory experiments. We also try to corroborate the relevance of social preferences in explaining human behavior. Experimental evidence shows clearly that there are many games in which Standard Nash Equilibrium1 (SNE) describes people's behavior quite well. However, there seem to be just as many other games in which laboratory behavior deviates substantially from the predictions of standard game theory. Obviously, there is a need for theoretical innovations that can explain the successes of game theory as well as its failures. Without doubt, theory has reacted to experimental evidence. There are several new theoretical approaches that can claim to have at least partial success in introducing superior concepts. Dynamic evolutionary approaches2 (e.g. replicator dynamics) often but not always converge to SNE. Quantal Response Equilibria and in particular the Logit Equilibrium (McKelvey and Palfrey, 1995, McKelvey and Palfrey, 1998 and Goeree and Holt, 2001) have been quite successful in explaining behavioral reactions due to parameter variations in games with identical SNEs. Finally, there is a third strand of research that was successful in explaining deviations from SNE. These are approaches of social preferences. The social preferences approach can be divided into at least three important substrands: theories of intentional reciprocity (Rabin, 1993 and Dufwenberg and Kirchsteiger, 2004), the inequity aversion approach (Bolton and Ockenfels, 2000 and Fehr and Schmidt, 1999) and recently a theory of social welfare preferences (Andreoni and Miller, 2002 and Charness and Rabin, 2002). In this paper we shall concentrate on the last two approaches. Bolton and Ockenfels as well as Fehr and Schmidt introduce concepts of inequity aversion. It is assumed that there exist people who dislike inequality and who actually sacrifice money to reduce it. Both concepts are particularly successful in describing laboratory behavior when they assume heterogeneous actors. Bolton and Ockenfels’ model is exclusively defined for heterogeneous subjects. Although Fehr and Schmidt's model can be used for homogeneous populations, all successful applications assume a mixture of inequity averse and strictly egoistic subjects; the latter being individuals with the standard utility functions in game theory. The approaches differ in the concrete definition of inequity aversion, and Bolton and Ockenfels allow for more general preference distributions of subjects. However, the general version of their model is somewhat more complicated, making it less suitable for direct application. It is no surprise that most further applications of the inequity aversion approach use the simpler Fehr and Schmidt variant. In the meantime inequity aversion has been challenged by numerous experiments (e.g. Kagel and Wolfe, 2001, Charness and Rabin, 2002 and Engelmann and Strobel, 2004). The most important alternative to inequity aversion has been presented by Charness and Rabin. They introduce a model of social welfare preferences with and without reciprocity. Social welfare preferences are characterized by individuals who give positive weight to aggregated surplus (i.e. if other people are better off, c.p., utility of individuals increase). The authors carried out 32 experiments and compared theoretical predictions of several social preference approaches with the experimental data. They concluded that social welfare preferences provide the best fit to the data. However, the comparison between social welfare preferences and the inequity aversion model is biased because Charness and Rabin ignore the fact that the most fruitful version of Fehr and Schmidt's inequity aversion model takes explicitly into account that there is a heterogeneity of preferences. In fact, in Fehr et al. (2005) as well as in Fehr et al. (2004) inequity averse actors are only a minority of the population, and the explanatory power of the model stems in particular from the interplay of strictly egoistic and inequity averse subjects. Charness and Rabin consider only a homogeneous population variant of the inequity aversion theory.3 In their own model of social welfare preferences they also assume a monomorphic population. In this paper we shall try to show that this limits the explanatory power of their model. Nevertheless, Charness and Rabin convincingly show that social welfare preferences might help to explain a lot of behavior in their 32 games. Fehr and Schmidt have shown the usefulness of modeling heterogeneous population equilibria with inequity averse and strictly egoistic agents. Charness and Rabin have shown some evidence for social welfare preferences and the relevance of reciprocity. This paper tries to combine these approaches and analyze whether this significantly increases explanatory power. The focus of this paper is the application of this basic idea. Therefore, the basic model has to be sufficiently tractable for direct applications in a wide variety of games. In fact, we are going to apply the model to 43 different games and show that its predictive accuracy is clearly greater than that of the isolated models. The reader should be well aware that the model presented in this paper is regarded as one single step in the development of operational models to explain experimental and field evidence. Its main purpose is to demonstrate the importance of heterogeneity of preferences. In Section 2 we shall introduce a very simple model with three types of preferences, two players, and an explicit consideration of reciprocity. In Section 3 this model is applied to all two-player experiments in Charness and Rabin. Its predictive accuracy is compared with that of the inequity aversion and the social welfare preference approach. In Section 4 the model is applied to eight games (each game is analyzed for two variants with identical Standard Nash Equilibria) taken from Goeree and Holt. Finally, in Section 5 there is a summary, some conclusions and some thoughts about future research.

. Conclusion The main purposes of this paper are to demonstrate the usefulness of social preferences in explaining economic behavior and, even more important, to show that heterogeneity of preferences can play an important role in explaining many deviations of laboratory behavior from standard game theoretical predictions. For these purposes, we introduce the concept of HSP Equilibrium and show that, compared with other well known approaches, it is quite able to explain behavior of subjects in the experiments of Charness and Rabin. The idea of HSP Equilibria integrates the competing approaches of Fehr and Schmidt (1999) and Charness and Rabin (2002) into a unified and tractable framework. According to HSP Equilibrium three types of players, strictly egoistic subjects, inequity averse agents and subjects with (social) welfare preferences, behave according to the corresponding (perfect) Bayesian Equilibria. HSP Equilibrium predictions are clearly superior to Standard Nash Equilibrium, the inequity aversion model (Fehr and Schmidt, 1999) and Charness and Rabin's model of social welfare preferences. Furthermore, it was shown that HSP Equilibrium can explain most “behavioral anomalies” (the “contradictions”) in Goeree and Holt. The overall impression is that the analytical combination of social preferences with heterogeneity in these preferences is a very productive way of understanding real behavior in laboratory experiments. HSP Equilibrium also explicitly takes into account negative reciprocity. Although this helps to get better predictions in a few games, reciprocity does not play a major role in most games that have been considered here. It remains unclear whether this achievement justifies the resulting analytical inconvenience. Finally, the HSP Equilibrium approach is far from perfect. There still remains an uncomfortably high level of “unexplained variation”. So where do we go from here? Presumably, there are two different ways one may try to make progress. The first one is to allow for even more than the three different types of players that are used in the HSP Equilibrium concept. For example, one can add subjects with competitive preferences (i.e. actors who always put negative weights on other people's payoffs). I have tried this procedure, but it turned out that the introduction of these preferences does not improve the predictive success of the approach. Furthermore, the more player types are integrated, the more tedious (i.e. less applicable) the analysis becomes. Therefore, I am quite pessimistic about this alternative for future research. Another way to proceed is to try to integrate heterogeneous social preferences in the Quantal response equilibrium framework. In an intuitive, appealing manner the proponents of this approach, in particular McKelvey and Palfrey as well as Goeree and Holt and their coauthors show that they can explain the behavioral consequences of parameter variations in many games and experiments. There is still a lot of room for improvement in their framework, too. Consequently, it looks like a natural next step to combine the idea of noisy decision making with the approach of heterogeneous social preferences.