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Reputation Effects Under Interdependent Values

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  • Harry Pei

Abstract

A patient player privately observes a persistent state and interacts with an infinite sequence of myopic uninformed players. The patient player is either a strategic type who maximizes his payoff or one of several commitment types who mechanically play the same action in every period. I focus on situations in which the uninformed player's best reply to a commitment action depends on the state and where the total probability of commitment types is sufficiently small. I show that the patient player's equilibrium payoff is bounded below his commitment payoff in some equilibria under some of his payoff functions. This is because he faces a trade‐off between building his reputation for commitment and signaling favorable information about the state. When players' stage‐game payoff functions are monotone‐supermodular, the patient player receives high payoffs in all states and in all equilibria. Under an additional condition on the state distribution, my reputation model yields a unique prediction on the patient player's equilibrium payoff and on‐path behavior.

Suggested Citation

  • Harry Pei, 2020. "Reputation Effects Under Interdependent Values," Econometrica, Econometric Society, vol. 88(5), pages 2175-2202, September.
    • Handle: RePEc:wly:emetrp:v:88:y:2020:i:5:p:2175-2202
    DOI: 10.3982/ECTA16584
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    References listed on IDEAS

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    Cited by:

    1. Harry Pei, 2020. "Reputation Building under Observational Learning," Papers 2006.08068, arXiv.org, revised Nov 2020.
    2. Pei, Harry, 2022. "Reputation for playing mixed actions: A characterization theorem," Journal of Economic Theory, Elsevier, vol. 201(C).
    3. Kaya, Ayça & Roy, Santanu, 2022. "Market screening with limited records," Games and Economic Behavior, Elsevier, vol. 132(C), pages 106-132.
    4. Yingkai Li & Harry Pei, 2020. "Equilibrium Behaviors in Repeated Games," Papers 2007.14002, arXiv.org, revised Feb 2021.
    5. Ekmekci, Mehmet & Maestri, Lucas, 2022. "Wait or act now? Learning dynamics in stopping games," Journal of Economic Theory, Elsevier, vol. 205(C).
    6. Mehmet Ekmekci & Hanzhe Zhang, 2021. "Reputational Bargaining with Ultimatum Opportunities," Papers 2105.01581, arXiv.org.
    7. Harry Pei, 2020. "Reputation for Playing Mixed Actions: A Characterization Theorem," Papers 2006.16206, arXiv.org, revised Apr 2021.
    8. Harry Pei, 2022. "Reputation Effects under Short Memories," Papers 2207.02744, arXiv.org, revised Jan 2023.
    9. Li, Yingkai & Pei, Harry, 2021. "Equilibrium behaviors in repeated games," Journal of Economic Theory, Elsevier, vol. 193(C).

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