Reputation for playing mixed actions: A characterization theorem

Harry Pei

Journal of Economic Theory, 2022, vol. 201, issue C

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.

Keywords: Reputation; Interdependent values; Supermartingales; Doob's Upcrossing Inequality (search for similar items in EconPapers)
JEL-codes: C73 D82 D83 (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:jetheo:v:201:y:2022:i:c:s002205312200028x

DOI: 10.1016/j.jet.2022.105438

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