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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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    References listed on IDEAS

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    3. Adam Brandenburger & Eddie Dekel, 2014. "Hierarchies of Beliefs and Common Knowledge," World Scientific Book Chapters,in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 2, pages 31-41 World Scientific Publishing Co. Pte. Ltd..
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    8. Adam Brandenburger & Amanda Friedenberg & H. Jerome Keisler, 2014. "Admissibility in Games," World Scientific Book Chapters,in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 7, pages 161-212 World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. Arieli, Itai, 2010. "Rationalizability in continuous games," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 912-924, September.
    2. repec:eee:matsoc:v:91:y:2018:i:c:p:6-16 is not listed on IDEAS
    3. Tsakas, Elias, 2014. "Epistemic equivalence of extended belief hierarchies," Games and Economic Behavior, Elsevier, vol. 86(C), pages 126-144.
    4. Andrés Perea & Willemien Kets, 2016. "When Do Types Induce the Same Belief Hierarchy?," Games, MDPI, Open Access Journal, vol. 7(4), pages 1-17, October.
    5. repec:eee:jetheo:v:169:y:2017:i:c:p:489-516 is not listed on IDEAS
    6. Chen, Yi-Chun & Takahashi, Satoru & Xiong, Siyang, 2014. "The robust selection of rationalizability," Journal of Economic Theory, Elsevier, vol. 151(C), pages 448-475.
    7. Grabiszewski, Konrad, 2010. "Kernel-based type spaces," Journal of Economic Theory, Elsevier, vol. 145(6), pages 2483-2495, November.
    8. 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.
    9. Itai Arieli, 2008. "Rationalizability in Continuous Games," Discussion Paper Series dp495, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    10. Willemien Kets, 2012. "Bounded Reasoning and Higher-Order Uncertainty," Discussion Papers 1547, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    11. Aviad Heifetz & Willemien Kets, 2012. "All Types Naive and Canny," Discussion Papers 1550, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    12. Dekel, Eddie & Siniscalchi, Marciano, 2015. "Epistemic Game Theory," Handbook of Game Theory with Economic Applications, Elsevier.

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