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Trust and betrayals: reputational payoffs and behaviors without commitment

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  • Pei, Harry

    (Department of Economics, Northwestern University)

Abstract

I study a repeated game in which a patient player wants to win the trust of some myopic opponents but can strictly benefit from betraying them. His benefit from betrayal is strictly positive and is his persistent private information. I characterize every type of patient player's highest equilibrium payoff and construct equilibria that attain this payoff. Since the patient player's Stackelberg action is mixed and motivating the lowest-benefit type to play mixed actions is costly, every type's highest equilibrium payoff is strictly lower than his Stackelberg payoff. In every equilibrium where the patient player approximately attains his highest equilibrium payoff, no type of the patient player plays stationary strategies or completely mixed strategies.

Suggested Citation

  • Pei, Harry, 2021. "Trust and betrayals: reputational payoffs and behaviors without commitment," Theoretical Economics, Econometric Society, vol. 16(2), May.
    • Handle: RePEc:the:publsh:4182
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    References listed on IDEAS

    as
    1. Roland Benabou & Guy Laroque, 1992. "Using Privileged Information to Manipulate Markets: Insiders, Gurus, and Credibility," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(3), pages 921-958.
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    Cited by:

    1. Starkov, Egor, 2023. "Only time will tell: Credible dynamic signaling," Journal of Mathematical Economics, Elsevier, vol. 109(C).
    2. Fudenberg, Drew & Gao, Ying & Pei, Harry, 2022. "A reputation for honesty," Journal of Economic Theory, Elsevier, vol. 204(C).
    3. Ehud Lehrer & Dimitry Shaiderman, 2022. "Markovian Persuasion with Stochastic Revelations," Papers 2204.08659, arXiv.org, revised May 2022.
    4. Pei, Harry, 2023. "Repeated communication with private lying costs," Journal of Economic Theory, Elsevier, vol. 210(C).

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    More about this item

    Keywords

    Reputation; no commitment type; equilibrium payoff; equilibrium behavior;
    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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