Imitation with asymmetric memory

Models of learning in games based on imitation have provided fundamental insights as the relevance of risk-dominance equilibria or perfectly competitive outcomes. It has also been shown, however, that the introduction of nontrivial memory in those models fundamentally alters the results. This paper further considers the effect of asymmetric memory length in the population. We focus on two classical results and find that, while asymmetric memory crucially affects equilibrium selection in coordination games, it reinforces the stability of perfectly competitive outcomes in oligopoly games. The latter result is generalized to aggregative games and to finite population ESS in symmetric games.