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The non-existence of a universal topological type space

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  • Pintér, Miklós

Abstract

The concept of types was introduced by Harsányi (1967-1968). In the literature there are two approaches for formalizing types, type spaces: the purely measurable and the topological models. In the former framework Heifetz and Samet (1998) showed that the universal type space exists and later Meier (2001) proved that it is complete. In this paper we examine the topological approach and conclude that there is no universal topological type space in the category of topological type spaces.

Suggested Citation

  • Pintér, Miklós, 2010. "The non-existence of a universal topological type space," Journal of Mathematical Economics, Elsevier, vol. 46(2), pages 223-229, March.
    • Handle: RePEc:eee:mateco:v:46:y:2010:i:2:p:223-229
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    References listed on IDEAS

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    1. MERTENS , Jean-François & SORIN , Sylvain & ZAMIR , Shmuel, 1994. "Repeated Games. Part B : The Central Results," LIDAM Discussion Papers CORE 1994021, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Heifetz, Aviad & Samet, Dov, 1999. "Coherent beliefs are not always types," Journal of Mathematical Economics, Elsevier, vol. 32(4), pages 475-488, December.
    3. Robert J. Aumann, 1999. "Interactive epistemology II: Probability," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(3), pages 301-314.
    4. Heifetz, Aviad & Samet, Dov, 1998. "Topology-Free Typology of Beliefs," Journal of Economic Theory, Elsevier, vol. 82(2), pages 324-341, October.
    5. 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..
    6. MEIER, Martin, 2001. "An infinitary probability logic for type spaces," LIDAM Discussion Papers CORE 2001061, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Miklós Pintér, 2005. "Type space on a purely measurable parameter space," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(1), pages 129-139, July.
    8. MERTENS , Jean-François & SORIN , Sylvain & ZAMIR , Shmuel, 1994. "Repeated Games. Part A : Background Material," LIDAM Discussion Papers CORE 1994020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. Heifetz, Aviad & Mongin, Philippe, 2001. "Probability Logic for Type Spaces," Games and Economic Behavior, Elsevier, vol. 35(1-2), pages 31-53, April.
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    Cited by:

    1. Heinsalu, Sander, 2014. "Universal type structures with unawareness," Games and Economic Behavior, Elsevier, vol. 83(C), pages 255-266.
    2. Pintér, Miklós, 2011. "Common priors for generalized type spaces," MPRA Paper 44818, University Library of Munich, Germany.
    3. Pintér, Miklós & Udvari, Zsolt, 2011. "Generalized type spaces," MPRA Paper 34107, University Library of Munich, Germany.

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