Learning to be fair

We study the process of equilibrium selection in games when players have social preferences of the type discussed, among others, by Rabin (1993) and Segal and Sobel (2007). To this end, we employ a standard noisy version of the best response dynamics. We obtain several results concerning some popular games such as the Prisoner's Dilemma and the Battle of the Sexes. We show that reciprocity may have a negative effect on the equilibrium selection process. When players are sufficiently concerned with reciprocity, the stochastically stable equilibrium in the Battle of the Sexes is inefficient. At the same time, the cooperative equilibrium in the Prisoner's Dilemma is never stochastically stable.

► We model the equilibrium selection process in psychological games using the Best response dynamics.
► We apply it to the model of reciprocal altruism developed in Rabin (1993) and Segal and Sobel (2007).
► We discover that reciprocal altruism may increase the probability that inefficient equilibria are selected.
► In the Battle of the Sexes, the stochastically stable equilibrium is efficient if players are selfish and inefficient when they are reciprocally altruistic.
► In the Prisoner's Dilemma, the cooperative, efficient equilibrium is never stochastically stable.