Folk theorems with Bounded Recall under(Almost) Perfect Monitoring

George Mailath and Wojciech Olszewski

No 1462, Discussion Papers from Northwestern University, Center for Mathematical Studies in Economics and Management Science

Abstract: 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.

Keywords: Repeated games; bounded recall strategies; folk theorem; imperfect monitoring (search for similar items in EconPapers)
JEL-codes: C72 C73 (search for similar items in EconPapers)
Date: 2008-03
New Economics Papers: this item is included in nep-gth
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Citations: View citations in EconPapers (1)

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Related works:
Journal Article: Folk theorems with bounded recall under (almost) perfect monitoring (2011)
Working Paper: Folk Theorems with Bounded Recall under (Almost) Perfect Monitoring (2008)
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