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Simple bounds on the value of a reputation

Author

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  • Olivier Gossner

    (PSE - Paris-Jourdan Sciences Economiques - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, LSE - London School of Economics and Political Science)

Abstract

We introduce entropy techniques to study the classical reputation model in which a long-run player faces a series of short-run players. The long-run player's actions are possibly imperfectly observed. We derive explicit lower and upper bounds on the equilibrium payoffs to the long-run player.

Suggested Citation

  • Olivier Gossner, 2011. "Simple bounds on the value of a reputation," Post-Print halshs-00654683, HAL.
    • Handle: RePEc:hal:journl:halshs-00654683
    DOI: 10.3982/ECTA9385
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00654683
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    References listed on IDEAS

    as
    1. Drew Fudenberg & David K. Levine, 2008. "Reputation And Equilibrium Selection In Games With A Patient Player," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 7, pages 123-142, World Scientific Publishing Co. Pte. Ltd..
    2. Drew Fudenberg & David K. Levine, 2008. "Maintaining a Reputation when Strategies are Imperfectly Observed," World Scientific Book Chapters, in: Drew Fudenberg & David K Levine (ed.), A Long-Run Collaboration On Long-Run Games, chapter 8, pages 143-161, World Scientific Publishing Co. Pte. Ltd..
    3. Milgrom, Paul & Roberts, John, 1982. "Predation, reputation, and entry deterrence," Journal of Economic Theory, Elsevier, vol. 27(2), pages 280-312, August.
    4. Ehud Lehrer & Sylvain Sorin, 1992. "A Uniform Tauberian Theorem in Dynamic Programming," Mathematics of Operations Research, INFORMS, vol. 17(2), pages 303-307, May.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Antonio Cabrales & Olivier Gossner & Roberto Serrano, 2013. "Entropy and the Value of Information for Investors," American Economic Review, American Economic Association, vol. 103(1), pages 360-377, February.
    2. 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.
    3. Hu, Ju, 2014. "Reputation in the presence of noisy exogenous learning," Journal of Economic Theory, Elsevier, vol. 153(C), pages 64-73.
    4. Harry Pei, 2020. "Reputation Effects Under Interdependent Values," Econometrica, Econometric Society, vol. 88(5), pages 2175-2202, September.
    5. Harry Pei, 2020. "Reputation Building under Observational Learning," Papers 2006.08068, arXiv.org, revised Nov 2020.
    6. Pei, Harry, 2022. "Reputation for playing mixed actions: A characterization theorem," Journal of Economic Theory, Elsevier, vol. 201(C).
    7. Antonio Cabrales & Olivier Gossner & Roberto Serrano, 2012. "The Appeal of Information Transactions," Working Papers 2012-13, Brown University, Department of Economics.
    8. Eduardo Faingold, 2020. "Reputation and the Flow of Information in Repeated Games," Econometrica, Econometric Society, vol. 88(4), pages 1697-1723, July.
    9. Ekmekci, Mehmet & Maestri, Lucas, 2022. "Wait or act now? Learning dynamics in stopping games," Journal of Economic Theory, Elsevier, vol. 205(C).
    10. Fudenberg, Drew & Gao, Ying & Pei, Harry, 2022. "A reputation for honesty," Journal of Economic Theory, Elsevier, vol. 204(C).
    11. Harry Pei, 2020. "Reputation for Playing Mixed Actions: A Characterization Theorem," Papers 2006.16206, arXiv.org, revised Apr 2021.
    12. Mailath, George J. & Samuelson, Larry, 2015. "Reputations in Repeated Games," Handbook of Game Theory with Economic Applications,, Elsevier.
    13. 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.
    14. Atakan, Alp Enver & Ekmekci, Mehmet, 2014. "Reputation in Repeated Moral Hazard Games," MPRA Paper 54427, University Library of Munich, Germany.
    15. Harry Pei, 2020. "Trust and Betrayals: Reputational Payoffs and Behaviors without Commitment," Papers 2006.08071, arXiv.org.
    16. Harry Pei, 2020. "Repeated Communication with Private Lying Cost," Papers 2006.08069, arXiv.org.
    17. Heski Bar-Isaac Jr. & Joyee Deb Jr., 2014. "(Good and Bad) Reputation for a Servant of Two Masters," American Economic Journal: Microeconomics, American Economic Association, vol. 6(4), pages 293-325, November.
    18. Pei, Harry, 2023. "Repeated communication with private lying costs," Journal of Economic Theory, Elsevier, vol. 210(C).
    19. Harry Pei, 2022. "Reputation Effects under Short Memories," Papers 2207.02744, arXiv.org, revised Jan 2023.
    20. 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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