Private Strategies in Finitely Repeated Games with Imperfect Public Monitoring (original) (raw)

Unattainable Payoffs for Repeated Games of Private Monitoring

SSRN Electronic Journal, 2000

We bound from the outside the set of sequential equilibrium payoffs in repeated games of private monitoring. The novelty in our approach is treating private histories as endogenous correlation devices. To do this, we develop a tractable new solution concept for standard repeated games with perfect monitoring: Markov Perfect Correlated Equilibrium generalizes the operator approach of Abreu, Pearce, and Stacchetti (1990) in a natural way to allow for correlated strategies. We show that for any monitoring structure, the set of sequential equilibrium payoffs of the repeated private monitoring game is always contained within the set of Markov Perfect Correlated Equilibrium payoffs of the analogous repeated game. Further, we explore two senses in which this bound is tight. * We are grateful for helpful comments from Pavlo Prokopovych (whom Lones advised in his 2006 Michigan PhD) and seminar participants at the Western Economic Association Meetings, Midwest Theory Conference, and the University of Michigan.

Repeated Games with Almost-Public Monitoring

Journal of Economic Theory, 2002

In repeated games with imperfect public monitoring, players can use public signals to coordinate their behavior, and thus support cooperative outcomes, but with private monitoring, such coordination may no longer be possible. Even though grim trigger is a perfect public equilibrium (PPE) in games with public monitoring, it often fails to be an equilibrium in arbitrarily close games with private monitoring. If a PPE has players' behavior conditioned only on finite histories, then it induces an equilibrium in all close-by games with private monitoring. This implies a folk theorem for repeated games with almost-public almost-perfect monitoring.

Unattainable Payofis for Repeated Games of Private Monitoring

2010

We bound from the outside the set of sequential equilibrium payoffs in repeated games of private monitoring. The novelty in our approach is treating private histories as endogenous correlation devices. To do this, we develop a tractable new solution concept for standard repeated games with perfect monitoring: Markov Perfect Correlated Equilibrium generalizes the operator approach of Abreu, Pearce, and Stacchetti (1990) in a natural way to allow for correlated strategies. We show that for any monitoring structure, the set of sequential equilibrium payoffs of the repeated private monitoring game is always contained within the set of Markov Perfect Correlated Equilibrium payoffs of the analogous repeated game. Further, we explore two senses in which this bound is tight. * We are grateful for helpful comments from Pavlo Prokopovych (whom Lones advised in his 2006 Michigan PhD) and seminar participants at the Western Economic Association Meetings, Midwest Theory Conference, and the University of Michigan.

Coordination failure in repeated games with almost-public monitoring

Theoretical Economics, 2006

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 (ie, there is a bound L such that in any period, the last L signals are sufficient to determine behavior). We show that, in games ...

Coordination Failure in Repeated Games with Almost-Public Monitoring, Second Version

SSRN Electronic Journal, 2005

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 publicmonitoring 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.

Efficient outcomes in repeated games with limited monitoring

Economic Theory, 2015

The Folk Theorem for infinitely repeated games with imperfect public monitoring implies that for a general class of games, nearly efficient payoffs can be supported in perfect public equilibrium (PPE) provided the monitoring structure is sufficiently rich and players are arbitrarily patient. This paper shows that for stage games in which actions of players interfere strongly with each other, exactly efficient payoffs can be supported in PPE even when the monitoring structure is not rich and players are not arbitrarily patient. The class of stage games we study abstracts many environments including resource sharing. Keywords repeated games • imperfect public monitoring • perfect public equilibrium • efficient outcomes • repeated resource allocation • repeated partnership • repeated contest Mathematics Subject Classification (2000) JEL C72 • C73 • D02 This research was supported by National Science Foundation (NSF) Grants No. 0830556, (van der Schaar, Xiao) and 0617027 (Zame) and by the Einaudi Institute for Economics and Finance (Zame). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of any funding agency.

On a private information game without pure strategy equilibria

Journal of Mathematical Economics, 1999

We present an example of a two-person game of private information in which there is no equilibrium in pure strategies. Our example satisfies all the hypotheses of the existence theorems present in the literature on the subject of pure strategy equilibria, except for the w x fact that the action set of each player is given by the interval y1,1. As such, it illustrates the limitations that pertain to the purification of equilibria in a standard setting.