آیا نوع دوستی تکاملی پایدار است

We develop an evolutionary approach to explain altruistic preferences. Given their preferences, individuals interact rationally with each other. By comparing the success of players with different preferences, we investigate whether evolution favors altruistic or selfish attitudes. The outcome depends on whether the individuals' interactions are strategic complements or substitutes. Altruism and self-interest are context dependent.

There is an abundance of observations showing that individuals do not always pursue self-interest: People risking their own life to rescue others, soldiers voluntarily going to war, the many forms of charity etc. These observations can be made consistent with standard economic theory by postulating utility functions that include the well-being of others in addition to one's own. Yet, this only rephrases the question of why individuals behave in this way. Instead of explaining altruistic behavior, one now has to explain why people sometimes have altruistic preferences. It is this question that we want to address. We adopt an evolutionary approach to investigate whether altruism may have evolved in humans through a process of natural or cultural selection. Formally, the degree of altruism is expressed by a preference parameter describing how much an individual cares for the success of others. The range of possible parameters includes pure self-interest as the special case where an agent's objective is identical to his private success. In the interaction with others, each player rationally selects a strategy to maximize his preferences. As a result, in equilibrium each player's effective success depends on the altruistic attitudes of all the involved players. This allows us to compare the success of players with different preference parameters. In an evolutionary environment, players with higher expected success are less likely to be eliminated. Since success is related to preferences, we can study the question of whether evolution favors altruistic or selfish attitudes. Altruism is said to be evolutionarily stable if it survives evolutionary selection. Instead of studying directly the evolution of behavior, which is the usual approach in evolutionary biology1 and in evolutionary game theory (see, e.g. Hammerstein and Selten, 1994), we consider rational behavior for given preferences. These preferences determine the players' behavior and their effective success via their effect on the outcome of strategic interactions. By assuming rational behavior and applying the concept of evolutionary stability (see Maynard Smith, 1982 and Frank, 1987) to preferences rather than to strategies, we endogenously determine preferences. Our approach thus offers a way of endogenizing individual objective functions, which neoclassical theory usually treats as exogenous.2 Our analysis of individual interactions yields two insights: First, a comparison of the interaction between altruists and the interaction between egoists reveals that the altruists achieve a higher material payoff than the egoists. This is so because altruistic preferences internalize some externalities in the game between the players. Second, when an altruist interacts with an egoist, the altruist's material payoff is lower than the egoist's payoff. This finding is in line with the conventional view that altruistic preferences reduce the individual's success, while at the same time increasing the opponent's success. The second result is often used as an argument that altruism cannot possibly evolve by natural selection. Yet, this argument does not directly address evolutionary considerations. For the process of natural selection, the relevant question is whether an egoistic mutant facing a population of altruists is more successful than the altruists among themselves. Altruism will be evolutionarily stable if an egoist in the interaction with an altruist receives a lower material payoff than an altruist. In our model, this depends on the strategic dependence between the players. Altruism turns out to be evolutionarily stable only if the game exhibits strategic complementarities in the sense of Bulow et al. (1985). If there is strategic substitutability, then the only evolutionarily stable equilibrium is one in which everybody is selfish. If there is strategic complementarity, one's partner, even if he is perfectly selfish, will treat one better if one is nice than if one is nasty. So it turns out that altruists may perform less well than their selfish partners, but still better than selfish individuals who have selfish partners. As a result, strategic complementarity supports altruism as an evolutionarily stable outcome. Our study thus suggests that preferences may be context-dependent. Situational factors may decide whether individuals are motivated by altruism or self-interest. As Frank, 1987 and Frank, 1988 and Schelling (1987) do, our analysis emphasizes the strategic role of preferences and emotions. A player's preferences affect not only his own equilibrium behavior, but also the behavior of his opponent. Depending on the type of interaction, this effect can be either beneficial or harmful for a player with altruistic preferences. As a result, natural selection favors altruism in the case of strategic complements but not in the case of strategic substitutes. The strategic role of preferences distinguishes our approach from alternative explanations of altruism that rely on `kin selection' arguments. These arguments show that evolution can sustain altruism between genetically linked individuals (see e.g. Bergstrom and Stark, 1993). An alternative approach to altruism is presented by Rotemberg (1994), who considers a two-stage decision process. In the first stage, selfish individuals choose whether they want to have altruistic preferences. In the second stage they interact with each other to maximize the preferences chosen in the first stage. Rotemberg notes that strategic complementarity in the second stage leads to the choice of some altruism in the first stage. In our view, the idea that preferences change in an evolutionary process is more appealing than Rotemberg's assumption that selfish individuals can decide to become true altruists. Also, our analysis provides an explicit relation between the degree of altruism and the degree of strategic complementarity. It turns out that evolutionarily stable altruism improves efficiency. Yet, it typically fails to induce a fully efficient outcome. With strategic substitutes, evolution does not support altruism even though it would increase efficiency. Section 2describes the interaction between individuals and defines their success resulting from their behavior. Section 3studies the interaction between egoistic players and discusses efficiency implications. Altruistic preferences are introduced in Section 4, where we also study the impact of preferences on the equilibrium outcome. Section 5investigates the evolutionary stability of altruism. In Section 6we extend our conclusions to a more general framework. Finally, Section 7concludes and discusses extensions

Unlike other evolutionary studies of altruistic behavior in strategic interaction, our indirect evolutionary approach does not deny rational decision making. In principle it allows for any hypotheses specifying how stimuli, for example, preferences, influence behavior. A process of natural or cultural selection then determines which stimuli emerge in the course of evolution. Our study employs the usual rationality assumptions of game theory to endogenize preferences, which neoclassical theory typically treats as exogenous. In this sense, the indirect evolutionary approach generalizes neoclassical theory. The most important finding of our study is that evolutionarily stable altruism depends on the type of strategic interaction, as expressed by the signs of the derivatives of material payoffs Ui(x,y). Although in our context altruism always produces more efficient outcomes, it is evolutionarily stable only if it induces the interaction partner to respond favorably. As the evolution of preferences depends on this strategic effect, one may expect altruism to mitigate inefficiencies only when interactions can be characterized as strategic complements. Another requirement for the evolution of altruism is related to the individuals' information about preferences. Our analysis employs the usual common knowledge assumption of game theory, which implies that the preference parameters α and β are commonly known. To illustrate the possible impact of incomplete information, consider a monomorphic population of altruists with parameter α<1. If now an egoistic mutant appears, each altruist will consider the probability of interacting with the mutant as negligible. With incomplete information, the egoist will be treated as an altruist and he will earn a higher material payoff than his altruistic encounter. As a result, altruism will become vulnerable against egoistic mutants. Our analysis, therefore, suggests that altruism is more likely to emerge in societies where individuals are not anonymous. For instance, altruism may be restricted to relatives and close friends. In contrast with the kin-selection argument, in our framework this happens not because family members are genetically linked but because they are better informed about each other. Nonetheless, even when preferences are not directly known, altruism may evolve if there are signals that indicate a person's attitude. In addition to the physical symptoms mentioned by Frank, 1987 and Frank, 1988, for instance, donations to charities might signal altrustic preferences. An egoist is less willing than an altruist to donate. If imitation is too costly for the egoist, donations can become a credible signal of altruism.