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On the Non-Existence of Reputation Effects in Two-Person Infinitely-Repeated Games

  • Jimmy Chan
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    Consider a two-person infinitely-repeated game in which one player is either a normal rational type or a commitment type that authomatically plays a fixed repeated-game strategy When her true type is private information a rational type may want to develop a reputation as a commitment type by mimicking the commitment type's actions But the uninformed player anticipating the behavior of the rational type may try to screen out the rational type by choosing an action which gives the rational type a low payoff when she mimics the commitment type My main result shows that for comparably patient players if the prior probability that the player is a commitment type is sufficiently small the screening process may take so long that the rational player does not benefit from developing a reputation In the case of equally patient players I show that the folk theorem holds even when both players possess a small amount of private information Schmidt (1994) and Cripps Schmidt and Thomas (1993) argue that reputation effects can rule out outcomes permitted by the folk theorem regardless of how small the prior probability that the player is a commitment type My results show that this argument only applies when one player is infinitely more patient than the other

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    Paper provided by The Johns Hopkins University,Department of Economics in its series Economics Working Paper Archive with number 441.

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    Date of creation: Apr 2000
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    Handle: RePEc:jhu:papers:441
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    1. David Kreps & Paul Milgrom & John Roberts & Bob Wilson, 2010. "Rational Cooperation in the Finitely Repeated Prisoners' Dilemma," Levine's Working Paper Archive 239, David K. Levine.
    2. Kalai, Ehud & Lehrer, Ehud, 1993. "Subjective Equilibrium in Repeated Games," Econometrica, Econometric Society, vol. 61(5), pages 1231-40, September.
    3. Cripps, Martin W. & Schmidt, Klaus M. & Thomas, Jonathan P., 1996. "Reputation in Perturbed Repeated Games," Journal of Economic Theory, Elsevier, vol. 69(2), pages 387-410, May.
    4. D. Fudenberg and E. Maskin., 1987. "Nash and Perfect Equilibria of Discounted Repeated Games," Economics Working Papers 8736, University of California at Berkeley.
    5. Marco Celentani, 1993. "Maintaining a Reputation Against A Long-Lived Opponent," Discussion Papers 1075R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    6. Fudenberg, Drew & Maskin, Eric, 1991. "On the dispensability of public randomization in discounted repeated games," Journal of Economic Theory, Elsevier, vol. 53(2), pages 428-438, April.
    7. Schmidt, Klaus M, 1993. "Reputation and Equilibrium Characterization in Repeated Games with Conflicting Interests," Econometrica, Econometric Society, vol. 61(2), pages 325-51, March.
    8. Cripps, Martin W. & Thomas, Jonathan P., 1997. "Reputation and Perfection in Repeated Common Interest Games," Games and Economic Behavior, Elsevier, vol. 18(2), pages 141-158, February.
    9. Fudenberg, Drew & Maskin, Eric, 1986. "The Folk Theorem in Repeated Games with Discounting or with Incomplete Information," Econometrica, Econometric Society, vol. 54(3), pages 533-54, May.
    10. Cripps, M.W. & Thomas, J.P., 1995. "The Folk Theorem in Repeated Games of Incomplete Information," The Warwick Economics Research Paper Series (TWERPS) 439, University of Warwick, Department of Economics.
    11. Ehud Lehrer & Ady Pauzner, 1999. "Repeated Games with Differential Time Preferences," Econometrica, Econometric Society, vol. 67(2), pages 393-412, March.
    12. Aumann, Robert J. & Sorin, Sylvain, 1989. "Cooperation and bounded recall," Games and Economic Behavior, Elsevier, vol. 1(1), pages 5-39, March.
    13. Cripps, Martin W & Thomas, Jonathan P, 1995. "Reputation and Commitment in Two-Person Repeated Games without Discounting," Econometrica, Econometric Society, vol. 63(6), pages 1401-19, November.
    14. Abreu, Dilip, 1988. "On the Theory of Infinitely Repeated Games with Discounting," Econometrica, Econometric Society, vol. 56(2), pages 383-96, March.
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