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

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  • Jimmy Chan

Abstract

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

Suggested Citation

  • Jimmy Chan, 2000. "On the Non-Existence of Reputation Effects in Two-Person Infinitely-Repeated Games," Economics Working Paper Archive 441, The Johns Hopkins University,Department of Economics.
  • Handle: RePEc:jhu:papers:441
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    References listed on IDEAS

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    1. Kreps, David M. & Milgrom, Paul & Roberts, John & Wilson, Robert, 1982. "Rational cooperation in the finitely repeated prisoners' dilemma," Journal of Economic Theory, Elsevier, vol. 27(2), pages 245-252, August.
    2. Schmidt, Klaus M, 1993. "Reputation and Equilibrium Characterization in Repeated Games with Conflicting Interests," Econometrica, Econometric Society, vol. 61(2), pages 325-351, March.
    3. Aumann, Robert J. & Sorin, Sylvain, 1989. "Cooperation and bounded recall," Games and Economic Behavior, Elsevier, vol. 1(1), pages 5-39, March.
    4. Abreu, Dilip, 1988. "On the Theory of Infinitely Repeated Games with Discounting," Econometrica, Econometric Society, vol. 56(2), pages 383-396, March.
    5. Cripps, Martin W & Thomas, Jonathan P, 1995. "Reputation and Commitment in Two-Person Repeated Games without Discounting," Econometrica, Econometric Society, vol. 63(6), pages 1401-1419, November.
    6. Fudenberg, Drew & Maskin, Eric, 1986. "The Folk Theorem in Repeated Games with Discounting or with Incomplete Information," Econometrica, Econometric Society, vol. 54(3), pages 533-554, May.
    7. 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.
    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. 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.
    10. Celentani, Marco, et al, 1996. "Maintaining a Reputation against a Long-Lived Opponent," Econometrica, Econometric Society, vol. 64(3), pages 691-704, May.
    11. Fudenberg, D. & Maskin, E., 1990. "Nash and perfect equilibria of discounted repeated games," Journal of Economic Theory, Elsevier, vol. 51(1), pages 194-206, June.
    12. 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.
    13. Kalai, Ehud & Lehrer, Ehud, 1993. "Subjective Equilibrium in Repeated Games," Econometrica, Econometric Society, vol. 61(5), pages 1231-1240, September.
    14. Ehud Lehrer & Ady Pauzner, 1999. "Repeated Games with Differential Time Preferences," Econometrica, Econometric Society, vol. 67(2), pages 393-412, March.
    15. 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.
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    Cited by:

    1. Atakan, Alp E. & Ekmekci, Mehmet, 2015. "Reputation in the long-run with imperfect monitoring," Journal of Economic Theory, Elsevier, vol. 157(C), pages 553-605.
    2. Monte, Daniel, 2016. "Reputation with one-sided monitoring: Ignorance as a commitment device," Economics Letters, Elsevier, vol. 144(C), pages 18-21.
    3. Dilip Abreu & David G. Pearce, 2006. "Bargaining, Reputation and Equilibrium Selection in Repeated Games with Contracts," Levine's Bibliography 321307000000000640, UCLA Department of Economics.
    4. Wolitzky, Alexander, 2011. "Indeterminacy of reputation effects in repeated games with contracts," Games and Economic Behavior, Elsevier, vol. 73(2), pages 595-607.

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