Contagion and state dependent mutations

Early results of evolutionary game theory showed that the risk dominant equilibrium is uniquely selected on the long run by the best response dynamics with mutation. Bergin and Lipman (1996) qualified this result by showing that for a given population size the evolutionary process can select any strict Nash equilibrium if the probability of choosing a nonbest reply is state-dependent. This paper shows that the unique selection of the risk dominant equilibrium is robust with respect to state dependent mutation in local interaction games. More precisely, for a given mutation structure there exists a minimum population size beyond which the risk dominant equilibrium is uniquely selected. Our result is driven by contagion and cohesion among players, which exists only in local interaction settings and favors the play of the risk dominant strategy. Our result strengthens the equilibrium selection result of evolutionary game theory