We study the steady states of a system in which players learn about the strategies their opponents are playing by updating their Bayesian priors in light of their observations.Players are matched at random to play a fixed extensive -form game, and each player observes the realized actions in his own matches, but not the intended off -path play of his opponents or the realized actions in other matches.If lifetimes are long and players are very patient, the steady state distribution of actions approximates those of a Nash equilibrium.

Self-confirming equilibrium differs from Nash equilibrium in allowing players to have incorrect beliefs about how their opponents would play off of the equilibrium path.We provide several examples of ways that self -confirming and Nash equilibria differ.In games with "identified deviators , " all self -confirming equilibrium outcomes can be generated by extensive -form correlated equilibria.In two-player games, self -confirming equilibria with "unitary beliefs" are Nash.1.