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Unattainable Payoffs for Repeated Games of Private Monitoring

24 Pages Posted: 2 Jul 2009 Last revised: 11 May 2010

Josh Cherry

University of Michigan at Ann Arbor - Department of Economics

Lones Smith

University of Wisconsin at Madison - Department of Economics

Date Written: May 11, 2010

Abstract

We bound from the outside the set of sequential equilibrium payoffs in repeated games of private monitoring. Our approach treats 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. This quantifies the dynamic strategic effect of correlation. 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. This bound can be made tight with a simple two-stage procedure.

The techniques we develop are tractable and apply to many important economic settings such as dynamic oligopoly, long-term partnerships, and relational contracting. In all cases, they provide the sharpest possible equilibrium payoff prediction that is agnostic about the monitoring structure.

Keywords: Repeated Games, Private Monitoring, Correlated Equilibrium

JEL Classification: C7

Suggested Citation

Cherry, Josh and Smith, Lones, Unattainable Payoffs for Repeated Games of Private Monitoring (May 11, 2010). Available at SSRN: https://ssrn.com/abstract=1427602 or http://dx.doi.org/10.2139/ssrn.1427602

Josh Cherry (Contact Author)

University of Michigan at Ann Arbor - Department of Economics ( email )

611 Tappan Street
Ann Arbor, MI 48109-1220
United States

Lones Smith

University of Wisconsin at Madison - Department of Economics ( email )

1180 Observatory Drive
Madison, WI 53706-1393
United States
608-263-3871 (Phone)
608-262-2033 (Fax)

HOME PAGE: http://www.lonessmith.com

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