Large nonanonymous repeated games

E. J. Green (1980, J. Econ. Theory 22, 155-182) and H. Sabourian (1990, J. Econ. Theory 51, 92-110) studied repeated games where a player's payoff depends on his actions and an anonymous aggregate outcome, and show that long-run players behave myopically in any equilibrium of such games. In this paper we extend these results to games where the aggregate outcome is not necessarily an anonymous function of players' actions, and where players' strategies may depend nonanonymously on signals of other players' behavior. Our argument also provides a conceptually simpler proof of Green and Sabourian's results, showing how their analysis is driven by general bounds on the number of pivotal players in a game.