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Imperfect Monitoring and Impermanent Reputations

  • Criminology
  • Law
  • Mathematics


Imperfect Monitoring and Impermanent Reputations Econometrica, Vol. 72, No. 2 (March, 2004), 407–432 IMPERFECT MONITORING AND IMPERMANENT REPUTATIONS BY MARTIN W. CRIPPS, GEORGE J. MAILATH, AND LARRY SAMUELSON1 We study the long-run sustainability of reputations in games with imperfect public monitoring. It is impossible to maintain a permanent reputation for playing a strategy that does not play an equilibrium of the game without uncertainty about types. Thus, a player cannot indefinitely sustain a reputation for noncredible behavior in the presence of imperfect monitoring. KEYWORDS: Reputation, imperfect monitoring, repeated games, commitment, Stackelberg types. 1. INTRODUCTION THE ADVERSE SELECTION APPROACH to reputations is central to the study of long-run relationships. In the finitely-repeated prisoners’ dilemma or chain- store game, for example, the intuitive expectation that cooperation or entry deterrence occurs in early rounds is inconsistent with equilibrium. However, incomplete information about a player’s characteristics can be exploited to support an equilibrium reputation for cooperating or fighting entry (Kreps, Milgrom, Roberts, and Wilson (1982), Kreps and Wilson (1982), and Milgrom and Roberts (1982)). In infinitely repeated games, the multiplicity of equilibria provided by the folk theorem contrasts with the intuitive attraction of equi- libria that provide relatively high payoffs. Reputation effects can again rescue intuition by imposing lower bounds on equilibrium payoffs (Fudenberg and Levine (1989, 1992)). This paper explores long-run reputation effects in games of imperfect mon- itoring with a long-lived player facing a sequence of short-lived players. In the absence of incomplete information about the long-lived player, her equilibrium payoff can be any value between her minmax payoff and an upper bound (in- dependent of her discount factor) strictly smaller than her Stackelberg payoff. However, when there is incomplete information about the long-lived

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