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Impermanent types and permanent reputations

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  • Ekmekci, Mehmet
  • Gossner, Olivier
  • Wilson, Andrea

Abstract

We study the impact of unobservable stochastic replacements for the long-run player in the classical reputation model with a long-run player and a series of short-run players. We provide explicit lower bounds on the Nash equilibrium payoffs of a long-run player, both ex-ante and following any positive probability history. Under general conditions on the convergence rates of the discount factor to one and of the rate of replacement to zero, both bounds converge to the Stackelberg payoff if the type space is sufficiently rich. These limiting conditions hold in particular if the game is played very frequently.

Suggested Citation

  • Ekmekci, Mehmet & Gossner, Olivier & Wilson, Andrea, 2012. "Impermanent types and permanent reputations," Journal of Economic Theory, Elsevier, vol. 147(1), pages 162-178.
    • Handle: RePEc:eee:jetheo:v:147:y:2012:i:1:p:162-178
    DOI: 10.1016/j.jet.2011.11.006
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    Cited by:

    1. Francisco Silva, 2020. "An informational Ponzi-scheme," Documentos de Trabajo 539, Instituto de Economia. Pontificia Universidad Católica de Chile..
    2. Fudenberg, Drew & Gao, Ying & Pei, Harry, 2022. "A reputation for honesty," Journal of Economic Theory, Elsevier, vol. 204(C).
    3. Liu, Qingmin & Skrzypacz, Andrzej, 2014. "Limited records and reputation bubbles," Journal of Economic Theory, Elsevier, vol. 151(C), pages 2-29.
    4. Daron Acemoglu & Alexander Wolitzky, 2012. "Cycles of Distrust: An Economic Model," Levine's Working Paper Archive 786969000000000502, David K. Levine.
    5. Sperisen, Benjamin, 2018. "Bounded memory and incomplete information," Games and Economic Behavior, Elsevier, vol. 109(C), pages 382-400.
    6. David K. Levine, 2021. "The Reputation Trap," Econometrica, Econometric Society, vol. 89(6), pages 2659-2678, November.
    7. Sharma, Priyanka, 2017. "Is more information always better? A case in credit markets," Journal of Economic Behavior & Organization, Elsevier, vol. 134(C), pages 269-283.
    8. Hu, Ju, 2014. "Reputation in the presence of noisy exogenous learning," Journal of Economic Theory, Elsevier, vol. 153(C), pages 64-73.
    9. Harbaugh, Rick & To, Ted, 2014. "Opportunistic discrimination," European Economic Review, Elsevier, vol. 66(C), pages 192-204.
    10. Silva, Francisco, 2022. "The value of uncertainty in determining an expert's source of expertise," Games and Economic Behavior, Elsevier, vol. 136(C), pages 379-388.
    11. Ju Hu, 2013. "Reputation in the Presence of Noisy Exogenous Learning," PIER Working Paper Archive 13-009, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    12. Renault, Jérôme & Solan, Eilon & Vieille, Nicolas, 2013. "Dynamic sender–receiver games," Journal of Economic Theory, Elsevier, vol. 148(2), pages 502-534.
    13. Fudenberg, Drew & Gao, Ying & Pei, Harry, 2022. "A reputation for honesty," Journal of Economic Theory, Elsevier, vol. 204(C).
    14. Wang, Yan & Yang, Jian & Qi, Lian, 2017. "A game-theoretic model for the role of reputation feedback systems in peer-to-peer commerce," International Journal of Production Economics, Elsevier, vol. 191(C), pages 178-193.
    15. Dilmé, Francesc, 2019. "Reputation building through costly adjustment," Journal of Economic Theory, Elsevier, vol. 181(C), pages 586-626.
    16. Eduardo Faingold, 2020. "Reputation and the Flow of Information in Repeated Games," Econometrica, Econometric Society, vol. 88(4), pages 1697-1723, July.
    17. Harry Pei, 2022. "Reputation Effects under Short Memories," Papers 2207.02744, arXiv.org, revised Jan 2023.
    18. Nuh Aygün Dalkıran, 2016. "Order of limits in reputations," Theory and Decision, Springer, vol. 81(3), pages 393-411, September.

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    More about this item

    Keywords

    Reputation; Repeated games; Impermanent types;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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