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When Do Types Induce the Same Belief Hierarchy?

Author

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  • Andrés Perea

    (EpiCenter and Department of Quantitative Economics, Maastricht University, P.O. Box 616, 6200 MD Maastricht, The Netherlands)

  • Willemien Kets

    (MEDS, Kellogg School of Management, Northwestern University, Evanston, IL 60208-2001, USA)

Abstract

Type structures are a simple device to describe higher-order beliefs. However, how can we check whether two types generate the same belief hierarchy? This paper generalizes the concept of a type morphism and shows that one type structure is contained in another if and only if the former can be mapped into the other using a generalized type morphism. Hence, every generalized type morphism is a hierarchy morphism and vice versa. Importantly, generalized type morphisms do not make reference to belief hierarchies. We use our results to characterize the conditions under which types generate the same belief hierarchy.

Suggested Citation

  • Andrés Perea & Willemien Kets, 2016. "When Do Types Induce the Same Belief Hierarchy?," Games, MDPI, vol. 7(4), pages 1-17, October.
    • Handle: RePEc:gam:jgames:v:7:y:2016:i:4:p:28-:d:79972
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    References listed on IDEAS

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    Cited by:

    1. Shuige Liu, 2018. "Characterizing Permissibility, Proper Rationalizability, and Iterated Admissibility by Incomplete Information," Papers 1811.01933, arXiv.org.
    2. Willemien Kets, 2012. "Bounded Reasoning and Higher-Order Uncertainty," Discussion Papers 1547, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    3. Perea, Andrés & Roy, Souvik, 2017. "A new epistemic characterization of ε-proper rationalizability," Games and Economic Behavior, Elsevier, vol. 104(C), pages 309-328.
    4. Paul Weirich, 2017. "Epistemic Game Theory and Logic: Introduction," Games, MDPI, vol. 8(2), pages 1-3, March.
    5. Shuige Liu, 2021. "Characterizing permissibility, proper rationalizability, and iterated admissibility by incomplete information," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(1), pages 119-148, March.

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