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Folk Theorems with Bounded Recall Under (Almost) Perfect Monitoring

30 Pages Posted: 2 Jun 2008  

George J. Mailath

University of Pennsylvania - Department of Economics

Wojciech Olszewski

Northwestern University - Department of Economics

Date Written: May 30, 2008

Abstract

A strategy profile in a repeated game has L bounded recall 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.

Keywords: repeated games, bounded recall strategies, folk theorem, imperfect monitoring

JEL Classification: C72,C73

Suggested Citation

Mailath, George J. and Olszewski, Wojciech, Folk Theorems with Bounded Recall Under (Almost) Perfect Monitoring (May 30, 2008). PIER Working Paper No. 08-019. Available at SSRN: https://ssrn.com/abstract=1139797 or http://dx.doi.org/10.2139/ssrn.1139797

George J. Mailath (Contact Author)

University of Pennsylvania - Department of Economics ( email )

160 McNeil Building
3718 Locust Walk
Philadelphia, PA 19104
United States
215-898-7749 (Phone)
215-573-2057 (Fax)

HOME PAGE: http://www.ssc.upenn.edu/~gmailath

Wojciech Olszewski

Northwestern University - Department of Economics ( email )

2003 Sheridan Road
Evanston, IL 60208
United States

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