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Equilibrium Refinement in Finite Action Evidence Games

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  • Shaofei Jiang

Abstract

Evidence games study situations where a sender persuades a receiver by selectively disclosing hard evidence about an unknown state of the world. Evidence games often have multiple equilibria. Hart et al. (2017) propose to focus on truth-leaning equilibria, i.e., perfect Bayesian equilibria where the sender discloses truthfully when indifferent, and the receiver takes off-path disclosure at face value. They show that a truth-leaning equilibrium is an equilibrium of a perturbed game where the sender has an infinitesimal reward for truth-telling. We show that, when the receiver's action space is finite, truth-leaning equilibrium may fail to exist, and it is not equivalent to equilibrium of the perturbed game. To restore existence, we introduce a disturbed game with a small uncertainty about the receiver's payoff. A purifiable truthful equilibrium is the limit of a sequence of truth-leaning equilibria in the disturbed games as the disturbances converge to zero. It exists and features a simple characterization. A truth-leaning equilibrium that is also purifiable truthful is an equilibrium of the perturbed game. Moreover, purifiable truthful equilibria are receiver optimal and give the receiver the same payoff as the optimal deterministic mechanism.

Suggested Citation

  • Shaofei Jiang, 2020. "Equilibrium Refinement in Finite Action Evidence Games," Papers 2007.06403, arXiv.org, revised Sep 2022.
    • Handle: RePEc:arx:papers:2007.06403
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    References listed on IDEAS

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    1. Sergiu Hart & Ilan Kremer & Motty Perry, 2017. "Evidence Games: Truth and Commitment," American Economic Review, American Economic Association, vol. 107(3), pages 690-713, March.
    2. Kreps, David M & Wilson, Robert, 1982. "Sequential Equilibria," Econometrica, Econometric Society, vol. 50(4), pages 863-894, July.
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