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

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

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, Second Version

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 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

Does Competitive Pricing Cause Market Breakdown under Extreme Adverse Selection?

We study market breakdown in a finance context under extreme adverse selection with and without competitive pricing. Adverse selection is extreme if for any price there are informed agent types with whom uninformed agents prefer not to trade. Market breakdown occurs when no trade is the only equilibrium outcome. We present a necessary and sufficient condition for market breakdown. If the condition holds, then trade is not viable. If the condition fails, then trade can occur under competitive pricing. There are environments in which the condition holds and others in which it fails.Adverse selection, market breakdown, separation, competitive pricing

Extreme Adverse Selection, Competitive Pricing, and Market Breakdown

Extreme adverse selection arises when private information has unbounded support, and market breakdown occurs when no trade is the only equilibrium outcome. We study extreme adverse selection via the limit behavior of a financial market as the support of private information converges to an unbounded support. A necessary and sufficient condition for market breakdown is obtained. If the condition fails, then there exists competitive market behavior that converges to positive levels of trade whenever it is first best to have trade. When the condition fails, no feasible (competitive or not) market behavior converges to positive levels of trade.Adverse selection, market breakdown, separation, competitive pricing

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