Monotone Imitation Dynamics in Large Populations

Abstract

We analyze a class of imitation dynamics with mutations for games with any finite number of actions, and give conditions for the selection of a unique equilibrium as the mutation rate becomes small and the population becomes large. Our results cover the multiple-action extensions of the aspiration-and-imitation process of Binmore and Samuelson [3] and the related processes proposed by Benaïm and Weibull [2] and Traulsen et al. [24], as well as the frequency-dependent Moran process studied by Fudenberg et al. [15]. We illustrate our results by considering the effect of the number of periods of repetition on the selected equilibrium in repeated play of the prisoner's dilemma when players are restricted to a small set of simple strategies.

Keywords: Equilibrium selection, Learning model, Limit distribution, Markov process, Prisoner's dilemma

JEL Classification: C62, C72, C73