A limit characterization of belief-free equilibrium payoffs in repeated games

The present paper provides a limit characterization of the payoff set supported by belief-free equilibria in repeated games with private monitoring, as the discount factor approaches one and the noise on private information vanishes. Contrary to the conjecture by Ely, Hörner, and Olszewski (2005), in many of the three-or-more player games, the payoff set is given by a union of product sets, as in two-player games. As an application of this result, the folk theorem is proved in N-player prisoner’s dilemma games. Journal of Economic Literature Classification Numbers: C72, C73, D82.