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When do type structures contain all hierarchies of beliefs?

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  • Friedenberg, Amanda

Abstract

Hierarchies of beliefs play a central role in game theory. In practice, they are modeled by type structures. This allows the analyst to describe hierarchies without explicitly specifying an infinite sequence of beliefs. The focus of this paper is type structures that contain all hierarchies of beliefs. Can the analyst identify these structures without explicit reference to hierarchies? That is, does there exist a test, defined on the type structure alone, so that the structure passes this test only if it contains all hierarchies of beliefs? This paper investigates one such test. The test is based on the concept of completeness [Brandenburger, A., 2003. On the existence of a 'complete' possibility structure. In: Basili, M., Dimitri, N., Gilboa, I. (Eds.), Cognitive Processes and Economic Behavior. Routledge, pp. 30-34], a concept that has played an important role in epistemic game theory.

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  • Friedenberg, Amanda, 2010. "When do type structures contain all hierarchies of beliefs?," Games and Economic Behavior, Elsevier, vol. 68(1), pages 108-129, January.
    • Handle: RePEc:eee:gamebe:v:68:y:2010:i:1:p:108-129
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    3. Fukuda, Satoshi, 2024. "The existence of universal qualitative belief spaces," Journal of Economic Theory, Elsevier, vol. 216(C).
    4. Arieli, Itai, 2010. "Rationalizability in continuous games," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 912-924, September.
    5. Andrés Perea & Willemien Kets, 2016. "When Do Types Induce the Same Belief Hierarchy?," Games, MDPI, vol. 7(4), pages 1-17, October.
    6. Willemien Kets, 2012. "Bounded Reasoning and Higher-Order Uncertainty," Discussion Papers 1547, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    7. Nicodemo De Vito, 2023. "Complete Conditional Type Structures (Extended Abstract)," Papers 2307.05630, arXiv.org.
    8. Ziegler, Gabriel & Zuazo-Garin, Peio, 2020. "Strategic cautiousness as an expression of robustness to ambiguity," Games and Economic Behavior, Elsevier, vol. 119(C), pages 197-215.
    9. Grabiszewski, Konrad, 2010. "Kernel-based type spaces," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2483-2495, November.
    10. Amanda Friedenberg & H. Jerome Keisler, 2021. "Iterated dominance revisited," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(2), pages 377-421, September.
    11. Battigalli Pierpaolo & Prestipino Andrea, 2013. "Transparent Restrictions on Beliefs and Forward-Induction Reasoning in Games with Asymmetric Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 13(1), pages 79-130, May.
    12. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications,, Elsevier.
    13. Keisler, H. Jerome & Lee, Byung Soo, 2023. "Common assumption of rationality," Journal of Mathematical Economics, Elsevier, vol. 109(C).
    14. Mounir, Angie & Perea, Andrés & Tsakas, Elias, 2018. "Common belief in approximate rationality," Mathematical Social Sciences, Elsevier, vol. 91(C), pages 6-16.
    15. Tsakas, Elias, 2014. "Epistemic equivalence of extended belief hierarchies," Games and Economic Behavior, Elsevier, vol. 86(C), pages 126-144.
    16. Perea, Andrés, 2017. "Forward induction reasoning and correct beliefs," Journal of Economic Theory, Elsevier, vol. 169(C), pages 489-516.
    17. Catonini, Emiliano & De Vito, Nicodemo, 2020. "Weak belief and permissibility," Games and Economic Behavior, Elsevier, vol. 120(C), pages 154-179.
    18. Andrés Perea & Arkadi Predtetchinski, 2019. "An epistemic approach to stochastic games," International Journal of Game Theory, Springer;Game Theory Society, vol. 48(1), pages 181-203, March.
    19. Chen, Yi-Chun & Takahashi, Satoru & Xiong, Siyang, 2014. "The robust selection of rationalizability," Journal of Economic Theory, Elsevier, vol. 151(C), pages 448-475.
    20. Keisler, H. Jerome & Lee, Byung Soo, 2011. "Common assumption of rationality," MPRA Paper 34441, University Library of Munich, Germany.
    21. Catonini, Emiliano, 2019. "Rationalizability and epistemic priority orderings," Games and Economic Behavior, Elsevier, vol. 114(C), pages 101-117.
    22. Guarino, Pierfrancesco & Ziegler, Gabriel, 2022. "Optimism and pessimism in strategic interactions under ignorance," Games and Economic Behavior, Elsevier, vol. 136(C), pages 559-585.
    23. Amanda Friedenberg & Martin Meier, 2017. "The context of the game," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(2), pages 347-386, February.
    24. Itai Arieli, 2008. "Rationalizability in Continuous Games," Discussion Paper Series dp495, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    25. Aviad Heifetz & Willemien Kets, 2012. "All Types Naive and Canny," Discussion Papers 1550, Northwestern University, Center for Mathematical Studies in Economics and Management Science.

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