Reputation in the Long-Run with Imperfect Monitoring
AbstractWe study an infinitely repeated game where two players with equal discount factors play a simultaneous-move stage game. Player one monitors the stagegame actions of player two imperfectly, while player two monitors the pure stagegame actions of player one perfectly. Player one’s type is private information and he may be a “commitment type,” drawn from a countable set of commitment types, who is locked into playing a particular strategy. Under a full-support assumption on the monitoring structure, we prove a reputation result for games with locally nonconflicting interests or games with strictly conflicting interests: if there is positive probability that player one is a particular type whose commitment payoff is equal to player one’s highest payoff, consistent with the players’ individual rationality, then a patient player one secures this type’s commitment payoff in any Bayes-Nash equilibrium of the repeated game. In contrast, if the type’s commitment payoff is strictly less than player one’s highest payoff consistent with the players’ individual rationality, then the worst perfect Bayesian equilibrium payoff for a patient player one is equal to his minimax payoff.
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Bibliographic InfoPaper provided by Northwestern University, Center for Mathematical Studies in Economics and Management Science in its series Discussion Papers with number 1506.
Date of creation: 01 Aug 2009
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Postal: Center for Mathematical Studies in Economics and Management Science, Northwestern University, 580 Jacobs Center, 2001 Sheridan Road, Evanston, IL 60208-2014
Web page: http://www.kellogg.northwestern.edu/research/math/
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