IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v201y2022ics002205312200028x.html
   My bibliography  Save this article

Reputation for playing mixed actions: A characterization theorem

Author

Listed:
  • Pei, Harry

Abstract

A patient player privately observes a persistent state that directly affects his opponents' payoffs, and can be one of the several commitment types that plays the same mixed action in every period. I characterize the set of environments under which the patient player obtains at least his commitment payoff in all equilibria regardless of his stage-game payoff function. Due to the presence of interdependent values, the patient player cannot guarantee his mixed commitment payoff by imitating the mixed commitment type, and small perturbations to a pure commitment action can significantly reduce the patient player's lowest equilibrium payoff.

Suggested Citation

  • Pei, Harry, 2022. "Reputation for playing mixed actions: A characterization theorem," Journal of Economic Theory, Elsevier, vol. 201(C).
    • Handle: RePEc:eee:jetheo:v:201:y:2022:i:c:s002205312200028x
    DOI: 10.1016/j.jet.2022.105438
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S002205312200028X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jet.2022.105438?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Olivier Gossner, 2011. "Simple Bounds on the Value of a Reputation," Econometrica, Econometric Society, vol. 79(5), pages 1627-1641, September.
    2. 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..
    3. 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..
    4. Ekmekci, Mehmet & Maestri, Lucas, 2019. "Reputation and screening in a noisy environment with irreversible actions," MPRA Paper 100885, University Library of Munich, Germany.
    5. Olivier Gossner, 2011. "Simple bounds on the value of a reputation," PSE-Ecole d'économie de Paris (Postprint) halshs-00654683, HAL.
    6. Mehmet Ekmekci & Leandro Gorno & Lucas Maestri & Jian Sun & Dong Wei, 2022. "Learning from Manipulable Signals," American Economic Review, American Economic Association, vol. 112(12), pages 3995-4040, December.
    7. Harry Pei, 2020. "Reputation Effects Under Interdependent Values," Econometrica, Econometric Society, vol. 88(5), pages 2175-2202, September.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ekmekci, Mehmet & Maestri, Lucas, 2022. "Wait or act now? Learning dynamics in stopping games," Journal of Economic Theory, Elsevier, vol. 205(C).
    2. Harry Pei, 2020. "Reputation for Playing Mixed Actions: A Characterization Theorem," Papers 2006.16206, arXiv.org, revised Apr 2021.
    3. Harry Pei, 2020. "Reputation Building under Observational Learning," Papers 2006.08068, arXiv.org, revised Nov 2020.
    4. Harry Pei, 2022. "Reputation Effects under Short Memories," Papers 2207.02744, arXiv.org, revised Jan 2023.
    5. Mailath, George J. & Samuelson, Larry, 2015. "Reputations in Repeated Games," Handbook of Game Theory with Economic Applications,, Elsevier.
    6. 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.
    7. Fudenberg, Drew & Gao, Ying & Pei, Harry, 2022. "A reputation for honesty," Journal of Economic Theory, Elsevier, vol. 204(C).
    8. Harry Pei, 2020. "Trust and Betrayals: Reputational Payoffs and Behaviors without Commitment," Papers 2006.08071, arXiv.org.
    9. Harry Pei, 2020. "Repeated Communication with Private Lying Cost," Papers 2006.08069, arXiv.org.
    10. Pei, Harry, 2023. "Repeated communication with private lying costs," Journal of Economic Theory, Elsevier, vol. 210(C).
    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. Atakan, Alp Enver & Ekmekci, Mehmet, 2014. "Reputation in Repeated Moral Hazard Games," MPRA Paper 54427, University Library of Munich, Germany.
    13. Drew Fudenberg & Ying Gao & Harry Pei, 2020. "A Reputation for Honesty," Papers 2011.07159, arXiv.org.
    14. 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.
    15. Eduardo Faingold, 2020. "Reputation and the Flow of Information in Repeated Games," Econometrica, Econometric Society, vol. 88(4), pages 1697-1723, July.
    16. Li, Yingkai & Pei, Harry, 2021. "Equilibrium behaviors in repeated games," Journal of Economic Theory, Elsevier, vol. 193(C).
    17. Joyee Deb & Yuhta Ishii, 2016. "Reputation Building under Uncertain Monitoring," Cowles Foundation Discussion Papers 2042, Cowles Foundation for Research in Economics, Yale University.
    18. Hu, Ju, 2014. "Reputation in the presence of noisy exogenous learning," Journal of Economic Theory, Elsevier, vol. 153(C), pages 64-73.
    19. Harry Pei, 2020. "Reputation Effects Under Interdependent Values," Econometrica, Econometric Society, vol. 88(5), pages 2175-2202, September.
    20. Antonio Cabrales & Olivier Gossner & Roberto Serrano, 2012. "The Appeal of Information Transactions," Working Papers 2012-13, Brown University, Department of Economics.

    More about this item

    Keywords

    Reputation; Interdependent values; Supermartingales; Doob's Upcrossing Inequality;
    All these keywords.

    JEL classification:

    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jetheo:v:201:y:2022:i:c:s002205312200028x. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622869 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.