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Robust refinement of rationalizability with arbitrary payoff uncertainty

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  • Chen, Yi-Chun
  • Takahashi, Satoru
  • Xiong, Siyang

Abstract

Following Fudenberg et al. (1988) and Dekel and Fudenberg (1990), we say that a refinement of (interim correlated) rationalizability is robust if it is prescribed by a solution correspondence that is upper hemicontinuous with respect to perturbations of higher-order beliefs. We characterize robust refinements of rationalizability subject to arbitrary common knowledge restrictions on payoffs. We demonstrate how the characterization pins down a novel family of robust refinements of rationalizability in arbitrary finite games as well as in specific economic examples such as first-price auctions and the Cournot competition. We also apply our characterization to study the critique raised by Weinstein and Yildiz (2007b) to the global-game equilibrium refinement approach. In terms of the model primitives, we provide a necessary and sufficient condition under which the Weinstein-Yildiz critique remains valid.

Suggested Citation

  • Chen, Yi-Chun & Takahashi, Satoru & Xiong, Siyang, 2022. "Robust refinement of rationalizability with arbitrary payoff uncertainty," Games and Economic Behavior, Elsevier, vol. 136(C), pages 485-504.
    • Handle: RePEc:eee:gamebe:v:136:y:2022:i:c:p:485-504
    DOI: 10.1016/j.geb.2022.10.009
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    Cited by:

    1. Chen, Yi-Chun & Kunimoto, Takashi & Sun, Yifei, 2023. "Continuous implementation with payoff knowledge," Journal of Economic Theory, Elsevier, vol. 209(C).

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