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.