Stochastic stability in a learning dynamic with best response to noisy play

We propose a learning dynamic with agents using samples of past play to estimate the distribution of other players' strategy choices and best responding to this estimate. To account for noisy play, estimated distributions over other players' strategy choices have full support in the other players' strategy sets for positive levels of noise and converge to the sampled distribution in the limit of vanishing noise. Recurrent classes of the dynamic process only contain admissible strategies and can be characterised by minimal CURB sets based on best responses to noisy play whenever the set of sampled distributions is sufficiently rich. In this case, the dynamic process will always end up in a set of strategies that contains the support of a (trembling hand) perfect equilibrium. If the perfect equilibrium is unique and in pure strategies, the equilibrium resembles the unique recurrent class of the dynamic process. We apply the dynamic process to learning in matching markets and sequential two player games with perfect information.