Perfect Public Equilibrium When Players Are Patient

We provide a characterization of the limit set of perfect public equilibrium payoffs of repeated games with imperfect public monitoring as the discount factor goes to one. Our result covers general stage games including those that fail a “full-dimensionality” condition that had been imposed in past work. It also provides a characterization of the limit set when the strategies are restricted in a way that endogenously makes the full-dimensionality condition fail, as in the strongly symmetric equilibrium studied by Abreu [Abreu, D., 1986. Extremal equilibria of oligopolistic supergames. J. Econ. Theory 39, 191–228] and Abreu et al. [Abreu, D., Pearce, D., Stacchetti, E., 1986. Optimal cartel equilibria with imperfect monitoring. J. Econ. Theory 39, 251–269]. Finally, we use our characterization to give a sufficient condition for the exact achievability of first-best outcomes. Equilibria of this type, for which all continuation payoffs lie on the Pareto frontier, have a strong renegotiation-proofness property: regardless of the history, players can never unanimously prefer another equilibrium.Economic

Perfect Public Equilibrium When Players Are Patient

The limit set of perfect public equilibrium payoffs of a repeated game as the discount factor goes to one is characterized, with examples, even when the full-dimensionality condition fails.

Learning from Private Information in Noisy Repeated Games

We study the perfect type-contingently public ex-post equilibrium (PTXE) of repeated games where players observe imperfect public signals of the actions played, and both the payoff functions and the map from actions to signal distributions depend on an unknown state. The PTXE payoffs when players are patient are determined by the solutions to a family of linear programming problems. Using this characterization, we develop conditions under which play can be as if the players have learned the state. We provide a sufficient condition for the folk theorem, and a characterization of the PTXE payoffs in games with a known monitoring structure.Economic

Cooperation cannot be sustained in a discounted repeated prisoners' dilemma with patient short and long run players

This study presents a modified version of the repeated discounted prisoners' dilemma with long and short-run players. In our setting a short-run player does not observe the history that has occurred before he was born, and survives into next phases of the game with a probability given by the current action profile in the stage game. Thus, even though it is improbable, a short-run player may live and interact with the long-run player for infinitely long amounts of time. In this model we prove that under a mild incentive condition on the stage game payoffs, the cooperative outcome path is not subgame perfect no matter how patient the players are. Moreover with an additional technical assumption aimed to provide a tractable analysis, we also show that payoffs arbitrarily close to that of the cooperative outcome path, cannot be obtained in equilibrium even with patient players

Reputation Effects

This article gives a brief introduction to reputation effects. A canonical model is described, the reputation bound result of Fudenberg and Levine (1989 1992) and the temporary reputation result of Cripps, Mailath, and Samuelson (2004, 2007) are stated and discussed.commitment, incomplete information, reputation bound, reputation effects

Reputation and perfection in repeated common interest games

We consider a wide class of repeated common interest games perturbed with one-sided incomplete information: one player (the informed player) might be a commitment type playing the Pareto dominant action. As discounting, which is assumed to be symmetric, and the prior probability of the commitment type go to zero, it is shown that the informed player can be held close to her minmax payoff even when perfection is imposed on the equilibrium