Games with Small Forgetfulness

While it is known how players may learn to play in a game they know, the issue of how their model of the game evolves over time is largely unexplored. This paper introduces small forgetfulness and shows that it may destabilize standard full-memory solutions. Players are repeatedly matched to play a game. After any match, they forget with infinitesimal probability the feasibility of any opponents' unobserved action, and they are reminded of all actions that they observe. During each period, they play an equilibrium consistent with their perception of the game. We show that the unique backward induction path drifts into a non-Nash, self-confirming equilibrium, in a class of extensive-form games that are fully characterized. Such a long-run prediction is always Pareto-undominated, and may Pareto dominate the original backward induction path. In one-shot simultaneous-move games, forgetfulness yields a refinement stronger than trembling hand perfection. Our results imply that there are games that players may never fully learn.

On-the-Job Signaling and Self-Confidence

The labour economics literature on signalling assumes workers know their own abilities. Well-settled experimental evidence contradicts that assumption: in the absence of hard facts, subjects are on average overconfident. First we show that in any equilibrium of any signalling model, overconfidence cannot make players better off. In order to obtain more detailed predictions, we then introduce a specific on-the-job signalling model. We show that at fully-separating equilibrium, overconfident workers choose tasks that are too onerous, fail them, and, dejected by such a failure, settle down for a position inferior to their potential. Such a pattern leads to permanent underemployment of workers, and inefficiency of the economy. For the case of unbiased workers uncertain about their own value, we determine a necessary and sufficient condition for the existence of fully-separating equilibrium.

Optimal Contracts under Generalized Verifiability Correspondences

Before playing a game, the players may sign a contract that prescibes not to take some actions. Following the methodology introduced in Bernheim and Whinston (1998), henceforth BW, this paper models verifiability as a correspondence mapping actually played actions that cannot be ruled out by a court. BW characterize optimal contracts in various settings both static and sequential, and show instances where optimal contracts must necessarily leave some verifiable prescriptions unspecified. This paper focuses on static settings. We extend the line of research of BW by considering also non-partitional and non-product correspondences, and by introducing different liability regimes in the framework. A complete characterization of optimal contracts is derived. We identify instances where, because of liability constraints, the optimal contracts must explicitely include unverifiable prescriptions. In some cases, the optimal outcome may be achieved only by signing a contract that cannot be enforced. Our analysis may be of some relevance for the foundations of incomplete contracts, as it shows that it is not necessarily the case that the players should sign an incomplete contract when complete contracts are unenforceable.

Imitation and Experimentation in a Changing Environment

This paper analyzes the equilibrium play in a random matching model with a changing environment. Under myopic decision making, players adopt imitation strategies similar to those observed in evolutionary models with sampling from past play in the population. If the players are patient, equilibrium strategies display elements of experimentation in addition to imitation. If the changes in the environment are infrequent enough, these strategies succeed in coordinating almost all of the players on the dominant action almost all of the time. The myopic rules, on the other hand, result in mis-coordination for a positive fraction of time.

Mediation and peace

This paper applies mechanism design to conflict resolution. We determine when and how unmediated communication and mediation reduce the ex ante probability of conflict in a game with asymmetric information. Mediation improves upon unmediated communication when the intensity of conflict is high, or when asymmetric information is significant. The mediator improves upon unmediated communication by not precisely reporting information to conflicting parties, and precisely, by not revealing to a player with probability one that the opponent is weak. Arbitrators who can enforce settlements are no more effective than mediators who only make non-binding recommendations

Strategic Information Transmission in Networks

We introduce a tractable model of cheap talk among players located on networks. In our model, a player can send a message to another player if and only if he is linked to him. We derive a sharp equilibrium and welfare characterization which reveals two basic insights. In equilibrium, the willingness of a player to communicate with a neighbor decreases with the number of opponents who communicate with the neighbor. The ex-ante equilibrium welfare of every player increases not only with the number of truthful reports transmitted in the network, but also when truthful reports are more evenly distributed across players. We apply our findings to the analysis of homophily in communities, to organization design, and to the study of endogenous network formation. Communication across communities decreases as communities become larger, and communication may be asymmetric: From large communities to small ones. In our set up, fully decentralized organizations maximize all players� welfare. Further, decentralized networks, where information may flow asymmetrically, endogenously form in equilibrium. Finally, we introduce the possibility of public communication in networks, and identify conditions under which public communication Pareto dominates private communication.

Mediation and Peace

This paper brings mechanism design to the study of conflict resolution in international relations. We determine when and how unmediated communication and mediation reduce the ex ante probability of conflict, in a simple game where conflict is due to asymmetric information. Unmediated communication helps reducing the chance of conflict as it allows conflicting parties to reveal their types and establish type-dependent transfers to avoid conflict. Mediation improves upon unmediated communication when the intensity of conflict is high, or when asymmetric information is large. The mediator improves upon unmediated communication by not precisely reporting information to conflicting parties, and precisely, by not revealing to a player with probability one that the opponent is weak. Surprisingly, in our set up, arbitrators who can enforce settlements are no more effective in reducing the probability of conflict than mediators who can only make non-binding recommendations.Mediation, War and Peace, Imperfect Information, Communication Games, Optimal Mechanism