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Hierarchies of beliefs and the belief-invariant Bayesian solution

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  • Tang, Qianfeng

Abstract

The belief-invariant Bayesian solution is a notion of correlated equilibrium in games with incomplete information proposed by Forges (1993), and hierarchy of beliefs over conditional beliefs is introduced by Ely and Peski (2006) in their study of interim independent rationalizability. We study the connection between the two concepts. We partially characterize the correlations embedded among type spaces with the same set of hierarchies of beliefs over conditional beliefs with partially correlating devices, which send correlated signals to players in a way that preserves each player’s belief about others’ types. Since the belief-invariant Bayesian solution is also implemented by such correlating devices, we then establish that it is invariant on equivalent type space.

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  • Tang, Qianfeng, 2015. "Hierarchies of beliefs and the belief-invariant Bayesian solution," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 111-116.
    • Handle: RePEc:eee:mateco:v:59:y:2015:i:c:p:111-116
    DOI: 10.1016/j.jmateco.2015.06.006
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    Cited by:

    1. Gabriel Ziegler, 2021. "Informational Robustness of Common Belief in Rationality," Papers 2103.02402, arXiv.org, revised Feb 2022.
    2. Tang, Qianfeng, 2015. "Interim partially correlated rationalizability," Games and Economic Behavior, Elsevier, vol. 91(C), pages 36-44.
    3. Ziegler, Gabriel, 2022. "Informational robustness of common belief in rationality," Games and Economic Behavior, Elsevier, vol. 132(C), pages 592-597.

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