Evolutionary stability in a reputational model of bargaining

A large and growing literature on reputation in games builds on the insight that the possibility of one or more players being boundedly rational can have significant effects on equilibrium behavior. This literature leaves unexplained the presence of behavioral players in the first place, as well as the particular forms of irrationality assumed and the population shares of the various types. In this paper we endogenize departures from rationality on the basis of an evolutionary stability criterion, under the assumption that rational players incur a cost which reflects the greater sophistication of their behavior. This cost may be arbitrarily small. Within the context of a reputational model of bargaining, we show that evolutionary stability necessitates the presence of behavioral players. It also places significant joint restrictions on the set of behavioral types that can coexist, their respective population shares, and the long run population share of rational players.