THE FOLK THEOREM WITH IMPERFECT PUBLIC INFORMATION

We study repeated games in which players observe a public outcome that imperfectly signals the actions played. We provide conditions guarant eeing that any feasible, individually rational payoff vector of the st age game can arise as a perfect equilibrium of the repeated game with sufficiently little discounting. The central condition requires that t here exist action profiles with the property that, for any two players , no two deviations-one by each player-give rise to the same probabili ty distribution over public outcomes. The results apply to principal-a gent, partnership, oligopoly, and mechanism-design models, and to one- shot games with transferable utilities.