Bayesian learning in normal form games

This paper studies myopic Bayesian learning processes for finite-player, finite-strategy normal form games. Initially, each player is presumed to know his own payoff function but not the payoff functions of the other players. Assuming that the common prior distribution of payoff functions satisfies independence across players, it is proved that the conditional distributions on strategies converge to a set of Nash equilibria with probability one. Under a further assumption that the prior distributions are sufficiently uniform, convergence to a set of Nash equilibria is proved for every profile of payoff functions, that is, every normal form game.