This paper examines repeated games in which each player observes a private and imperfect signal on the actions played and in which players are allowed to communicate using public messages. Providing incentives for players to reveal their observations generate revelation constraints which, combined with signal imperfections, may be a source of inefficiencies. However, the author shows that, by delaying the revelation of their observations, players may reduce the cost of deterring deviations. With at least three players, he obtains a Nash threat version of the folk theorem. With two players, the author shows that an efficient outcome can (almost) always be approximated.

The presence of obstinate types in bargaining has been shown to alter dramatically the bargaining equilibrium strategies and outcomes. This paper shows that outside options may cancel out the effect of obstinacy in bargaining. When parties have access to stationary outside options, we show that when opting out is preferable to accepting the inflexible demand of the other party, there is a unique Perfect Bayesian Equilibrium in which each party reveals himself as rational as soon as possible. A similar conclusion holds when outside options may only be available at a later date or when only one party has access to an outside option.

The coalitional Nash bargaining solution is defined to be the core allocation for which the product of players' payoffs is maximal. We consider a non-cooperative model with discounting in which one team may form and every player is randomly selected to make a proposal in every period. The grand team, consisting of all players, generates the largest surplus. But a smaller team may form. We show that as players get more patient if an efficient and stationary equilibrium exists, it must deliver payoffs that correspond to the coalitional Nash bargaining solution. We also characterize when an efficient and stationary equilibrium exists, which requires conditions that go beyond the nonemptiness of the core.