Ž.
GAMES AND ECONOMIC BEHAVIOR
18, 141᎐158 1997
ARTICLE NO
. GA970520
Reputation and Perfection in Repeated Common
Interest Games*
Martin W. Cripps and Jonathan P. Thomas
Department of Economics, Uni
¨
ersity of Warwick, Co
¨
entry CV4 7AL, England
Received June 18, 1993
We consider a wide class of repeated common interest games perturbed with
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one-sided incomplete information: one player the informed player might be a
commitment type playing the Pareto dominant action. As discounting, which is
assumed to be symmetric, and the prior probability of the commitment type go to
zero, it is shown that the informed player can be held close to her minmax payoff
even when perfection is imposed on the equilibrium. Journal of Economic Literature
Classification Numbers: C73, D83.
ᮊ
1997 Academic Press
1. INTRODUCTION
Two-person common interest games are defined as games with a strongly
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Pareto-dominant payoff vector Aumann & Sorin, 1989 . If the game is
repeated infinitely often and if the players are patient, it might be expected
that they would be able to coordinate and receive average payoffs close to
the dominant payoff vector. It is, however, an implication of the Folk
theorem for repeated games that there exist equilibria in which patient
players receive payoffs substantially below the dominant payoff vector.
Moreover, even imposing subgame perfection does not alter this general
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result Fudenberg and Maskin, 1986 . That such inefficient equilibria can
survive in the long run when players are very patient seems counterintu-
itive, and in this paper we shall investigate whether perfection, when
applied to a simple ‘‘reputation’’ model, can lead to such undesirable
equilibria being eliminated.
Specifically, we shall consider perturbing a common interest game with
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only the possibility that one of the players, say player 1, might be a type
committed to playing a cooperative action, that is, the action correspond-
*We express our gratitude to Klaus Schmidt, an associate editor, and an anonymous
referee for useful comments. Our thanks are also due to seminar participants at Bonn,
Edinburgh, Erasmus, Exeter, and Tilburg for comments. All remaining errors are our
responsibility.
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ᮊ 1997 by Academic Press
All rights of reproduction in any form reserved.