Learning in Repeated Games without Repeating the Game

This paper extends the convergence result on Bayesian learning in Kalai and Lehrer (1993a, 1993b) to a class of games where players have a payoff function continuous for the product topology. Provided that 1) every player maximizes her expected payoff against her own beliefs, 2) every player updates her beliefs in a Bayesian manner, and 3) prior beliefs other players’ strategies have a grain of truth, we show that after some finite time the equilibrium outcome of the above game is arbitrarily close to a Nash equilibrium. Those assumptions are shown to be tight.