Stochastic better-reply dynamics in finite games

In this paper, we analyze a model where individuals from finite populations are repeatedly drawn to play a finite game and in every period choose a weakly better reply to a sample distribution from a finite history of past play. For all finite games and sufficiently incomplete information, we prove convergence to minimal sets closed under better replies. This result complements previous findings in a deterministic continuous-time framework and implies convergence to strict Nash equilibria in many well-known classes of games.