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Maintaining a Reputation against a Long-Lived Opponent

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Abstract

We analyze in a game between a patient player 1 and a non-myopic but less patient opponent, player 2. We assume that Player 1's type is private information and that players do not directly observe each other's action but rather see an imperfect signal of it. We show that in any Nash equilibrium of the game player 1 will get almost the largest payoff consistent with player 2 choosing a best response in a finite truncation of the game. If the discount factor of player 2 is sufficiently large, then player 1 will get approximately the maximum payoff consistent with player 2 getting at least his pure strategy minmax payoff.
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  • Celentani, Marco, et al, 1996. "Maintaining a Reputation against a Long-Lived Opponent," Econometrica, Econometric Society, vol. 64(3), pages 691-704, May.
    • Handle: RePEc:ecm:emetrp:v:64:y:1996:i:3:p:691-704
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    Cited by:

    1. Cripps, Martin W. & Mailath, George J. & Samuelson, Larry, 2007. "Disappearing private reputations in long-run relationships," Journal of Economic Theory, Elsevier, vol. 134(1), pages 287-316, May.
    2. Harasser, Andreas, 2014. "Information asymmetry and reentry," Economics Letters, Elsevier, vol. 123(2), pages 118-121.
    3. 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.
    4. Haag, Matthew & Lagunoff, Roger, 2007. "On the size and structure of group cooperation," Journal of Economic Theory, Elsevier, vol. 135(1), pages 68-89, July.
    5. Ely, Jeffrey & Fudenberg, Drew & Levine, David K., 2008. "When is reputation bad?," Games and Economic Behavior, Elsevier, vol. 63(2), pages 498-526, July.
    6. Hausken, Kjell, 2005. "The battle of the sexes when the future is important," Economics Letters, Elsevier, vol. 87(1), pages 89-93, April.
    7. Sorin, Sylvain, 1999. "Merging, Reputation, and Repeated Games with Incomplete Information," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 274-308, October.
    8. Yuval Heller & Erik Mohlin, 2018. "Observations on Cooperation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(4), pages 2253-2282.
    9. Jung, Hanjoon Michael, 2018. "Receiver’s dilemma," Journal of Mathematical Economics, Elsevier, vol. 75(C), pages 116-124.
    10. Hausken, Kjell, 2007. "Reputation, incomplete information, and differences in patience in repeated games with multiple equilibria," Economics Letters, Elsevier, vol. 97(2), pages 138-144, November.
    11. 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.
    12. Fudenberg, Drew & Gao, Ying & Pei, Harry, 2022. "A reputation for honesty," Journal of Economic Theory, Elsevier, vol. 204(C).
    13. Lu, Yang K., 2013. "Optimal policy with credibility concerns," Journal of Economic Theory, Elsevier, vol. 148(5), pages 2007-2032.
    14. Mailath, George J. & Samuelson, Larry, 2015. "Reputations in Repeated Games," Handbook of Game Theory with Economic Applications,, Elsevier.
    15. 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.
    16. Sandroni, Alvaro, 2000. "Reciprocity and Cooperation in Repeated Coordination Games: The Principled-Player Approach," Games and Economic Behavior, Elsevier, vol. 32(2), pages 157-182, August.
    17. Bahbouhi, Jalal Eddine & Moussa, Najem, 2017. "Prisoner’s dilemma game model for e-commerce," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 128-144.
    18. Fong, Yuk-fai & Surti, Jay, 2009. "The optimal degree of cooperation in the repeated Prisoners' Dilemma with side payments," Games and Economic Behavior, Elsevier, vol. 67(1), pages 277-291, September.
    19. Mehmet Ekmekci & Alp Atakan, 2009. "Reputation with Long Run Players and Imperfect Observation," 2009 Meeting Papers 222, Society for Economic Dynamics.
    20. Monte, Daniel, 2016. "Reputation with one-sided monitoring: Ignorance as a commitment device," Economics Letters, Elsevier, vol. 144(C), pages 18-21.
    21. Wolitzky, Alexander, 2011. "Indeterminacy of reputation effects in repeated games with contracts," Games and Economic Behavior, Elsevier, vol. 73(2), pages 595-607.
    22. Joyee Deb & Yuhta Ishii, 2016. "Reputation Building under Uncertain Monitoring," Cowles Foundation Discussion Papers 2042, Cowles Foundation for Research in Economics, Yale University.

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    JEL classification:

    • I10 - Health, Education, and Welfare - - Health - - - General

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