Payoff externalities and social learning

We study a social learning model with payoff externalities in which one of two state-dependent games is chosen at random and then played repeatedly by a different group of agents. Each “generation” observes the history of actions and receives conditionally independent private signals about the realized game. We show that with probability one, the play converges to the set of equilibria of an appropriate convex combination of the two state games. We provide a necessary and sufficient condition on the private signal distribution for asymptotic learning and show that in some cases asymptotic learning holds for a wide range of bounded private signals.