Sampling Best Response Dynamics and Deterministic Equilibrium Selection," mimeo

We consider a model of evolution in games in which a revising agent observes the actions of a random number of randomly sampled opponents and then chooses a best response to the distribution of actions in the sample. We provide a con-dition on the distribution of sample sizes under which an iterated p-dominant equilibrium is almost globally asymptotically stable under these dynamics. We show under an additional condition on the sample size distribution that in super-modular games, an almost globally asymptotically stable state must be an iterated p-dominant equilibrium. Since our selection results are for deterministic dynam-ics, any selected equilibrium is reached quickly; the long waiting times associated with equilibrium selection in stochastic stability models are absent