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.

This paper identifies a source of gradualism in bargaining and contribution games. In the bargaining games we examine, each party can opt out at any time, and the outside option outcome is assumed to depend on the offers made in the negotiation phase. Specifically, we assume that (1) making a concession in the negotiation phase increases the other party's outside option pay-off and (2) the outside option outcome induces an efficiency loss as compared with a negotiated agreement. The main finding is that the mere presence of such history-dependent outside options forces equilibrium concessions in the negotiation phase to be gradual, and the degree of gradualism is characterized. The model also applies to contribution games in which the outside option may be interpreted as the option to implement a partial project using the total contributions made so far.

This paper identifies a source of gradualism in bargaining and contribution games. In the bargaining games we examine, each party can opt out at any time, and the outside option outcome is assumed to depend on the offers made in the negotiation phase. Specifically, we assume that (1) making a concession in the negotiation phase increases the other party's outside option pay-off and (2) the outside option outcome induces an efficiency loss as compared with a negotiated agreement. The main finding is that the mere presence of such history-dependent outside options forces equilibrium concessions in the negotiation phase to be gradual, and the degree of gradualism is characterized. The model also applies to contribution games in which the outside option may be interpreted as the option to implement a partial project using the total contributions made so far.

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.

Quitting rights play a major role in many economic interactions, whether in the precontractual phase or after contracts have been signed. Clearly, no party can be forced to sign a contract if she is unwilling to, thus implying that quitting rights can be exerted at the ex ante stage when no contract has been signed. But, quitting rights can also be exerted after explicit contracts have been signed in a number of instances. For example, most labor contracts allow employees to leave their job if they want to. Also, quitting rights may be asymmetric across agents as labor contracts illustrate. (Employers are generally constrained in their ability to replace their employees.)

There is ample evidence that emotions affect performance. Positive emotions can improve performance, while negative ones can diminish it. For example, the fears induced by the possibility of failure or of negative evaluations have physiological consequences (shaking, loss of concentration) that may impair performance in sports, on stage, or at school. There is also ample evidence that individuals have distorted recollection of past events and distorted attributions of the causes of success or failure. Recollection of good events or successes is typically easier than recollection of bad ones or failures. Successes tend to be attributed to intrinsic aptitudes or effort, while failures are attributed to bad luck. In addition, these attributions are often reversed when judging the performance of others. The objective of this paper is to incorporate the phenomenon that emotions affect performance into an otherwise standard decision theoretic model and show that in a world where performance depends on emotions, biases in information processing enhance welfare.

We study collective search processes in which members of a committee decide whether to accept the current proposal or continue searching. The acceptance decision is made according to majority rule. We study which members have more impact on the decision, as well as the degree of randomness of the decision. When proposals vary along a single dimension, the acceptance set is small, and at most two members determine the outcome whatever the majority rule. When proposals vary along many dimensions, the acceptance set is large except under unanimity and all members affect the distribution of decisions. Various implications are drawn.

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.

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