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Reputation for playing mixed actions: A characterization theorem

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  • 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
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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. Olivier Gossner, 2011. "Simple bounds on the value of a reputation," PSE-Ecole d'économie de Paris (Postprint) halshs-00654683, HAL.
    4. 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.
    5. Olivier Gossner, 2011. "Simple Bounds on the Value of a Reputation," Econometrica, Econometric Society, vol. 79(5), pages 1627-1641, September.
    6. Harry Pei, 2020. "Reputation Effects Under Interdependent Values," Econometrica, Econometric Society, vol. 88(5), pages 2175-2202, September.
    7. Ekmekci, Mehmet & Maestri, Lucas, 2019. "Reputation and screening in a noisy environment with irreversible actions," MPRA Paper 100885, University Library of Munich, Germany.
    Full references (including those not matched with items on IDEAS)

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    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

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