Incentive Compatibility and Differentiability New Results and Classic Applications

We provide several generalizations of Mailath's (1987) result that in games of asymmetric information with a continuum of types incentive compatibility plus separation implies differentiability of the informed agent's strategy. The new results extend the theory to classic models in finance such as Leland and Pyle (1977), Glosten (1989), and DeMarzo and Duffie (1999), that were not previously covered

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

Folk theorems with Bounded Recall under(Almost) Perfect Monitoring

A strategy profile in a repeated game has bounded recall L if play under the profile after two distinct histories that agree in the last L periods is equal. Mailath and Morris (2002, 2006) proved that any strict equilibrium in bounded-recall strategies of a game with full support public monitoring is robust to all perturbations of the monitoring structure towards private monitoring (the case of almost-public monitoring), while strict equilibria in unbounded-recall strategies are typically not robust. We prove that the perfect-monitoring folk theorem continues to hold when attention is restricted to strategies with bounded recall and the equilibrium is essentially required to be strict. The general result uses calendar time in an integral way in the construction of the strategy profile. If the players’ action spaces are sufficiently rich, then the strategy profile can be chosen to be independent of calendar time. Either result can then be used to prove a folk theorem for repeated games with almost-perfect almost-public monitoring.Repeated games, bounded recall strategies, folk theorem, imperfect monitoring

Disappearing private reputations in long-run relationships

For games of public reputation with uncertainty over types and imperfect public monitoring, Cripps et al. [Imperfect monitoring and impermanent reputations, Econometrica 72 (2004) 407–432] showed that an informed player facing short-lived uninformed opponents cannot maintain a permanent reputation for playing a strategy that is not part of an equilibrium of the game without uncertainty over types. This paper extends that result to games in which the uninformed player is long-lived and has private beliefs, so that the informed player's reputation is private. The rate at which reputations disappear is uniform across equilibria and reputations also disappear in sufficiently long discounted finitely repeated games

Coordination Failure in Repeated Games with Almost-Public Monitoring

Some private-monitoring games, that is, games with no public histories, can have histories that are almost public. These games are the natural result of perturbing public monitoring games towards private monitoring. We explore the extent to which it is possible to coordinate continuation play in such games. It is always possible to coordinate continuation play by requiring behavior to have bounded recall (i.e., there is a bound L such that in any period, the last L signals are sufficient to determine behavior). We show that, in games with general almost-public private monitoring, this is essentially the only behavior that can coordinate continuation play.repeated games, private monitoring, almost-public monitoring, coordination, bounded recall

Folk Theorems with Bounded Recall under (Almost) Perfect Monitoring, Third Version

We prove the perfect-monitoring folk theorem continues to hold when attention is restricted to strategies with bounded recall and the equilibrium is essentially required to be strict. As a consequence, the perfect monitoring folk theorem is shown to be behaviorally robust under almost-perfect almost-public monitoring. That is, the same specification of behavior continues to be an equilibrium when the monitoring is perturbed from perfect to highly-correlated private.Repeated games, bounded recall strategies, folk theorem,imperfect monitoring

Coordination Failure in Repeated Games with Almost-Public Monitoring

Some private-monitoring games, that is, games with no public histories, can have histories that are almost public. These games are the natural result of perturbing public-monitoring games towards private monitoring. We explore the extent to which it is possible to coordinate continuation play in such games. It is always possible to coordinate continuation play by requiring behavior to have bounded recall (i.e., there is a bound L such that in any period, the last L signals are sufficient to determine behavior). We show that, in games with general almost-public private monitoring, this is essentially the only behavior that can coordinate continuation play.Repeated games, Private monitoring, Almost-public monitoring, Coordination, Bounded recall

Social Assets

We present a model incorporating both social and economic components, and analyze their interaction. The notion of a social asset, an attribute that has value only because of the social institutions governing society, is introduced. In the basic model, agents match on the basis of income and unproductive attributes. An attribute has value in some equilibrium social institutions (matching patterns), but not in others. We then show that productive attributes (such as education) can have their value increased above their inherent productive value by some social institutions, leading to the notion of the social value of an asset.Social assets, social capital, social arrangements, nonmarket interactions, social norms