Mutation rates and equilibrium selection under stochastic evolutionary dynamics

Abstract

We examine an evolutionary model in which the mutation rate varies with the strategy. Bergin and Lipman (Econometrica 64:943-956, 1996) show that equilibrium selection using stochastic evolutionary processes depends on the specification of mutation rates. We offer a characterization of how mutation rates determine the selection of Nash equilibria in 2 × 2 symmetric coordination games for single and double limits of the small mutation rate and the large population size. We prove that the restrictions on mutation rates which ensure that the risk-dominated equilibrium is selected are the same for both orders of limits.

Stochastic stability in the large population and small mutation limits for coordination games

“…Several studies, e.g. [23,27], have applied binomial large deviation theorem to two-strategy games, where choices are binary, in order to characterize stochastically stable states in the large population limit. We attempt to apply the multinomial version to games with more than two strategies, and it turns out to be successful.…”

“…of Wisconsin-Madison. This paper has been built upon [27], which was my first paper supervised by Bill. The author is also grateful to the two anonymous referees, Christoph Kuzmics, Dai Zusai and participants at Evolutionary Dynamics and Market Behavior Workshop at University of Bonn and Econometric Society European Meeting 2013 for their helpful comments.…”