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The non-existence of a universal topological type space

  • Pintér, Miklós
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    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.

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    File URL: http://www.sciencedirect.com/science/article/B6VBY-4XRCRX5-3/2/a9d0cce62b43f5531bcfe314feebe0a9
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    Article provided by Elsevier in its journal Journal of Mathematical Economics.

    Volume (Year): 46 (2010)
    Issue (Month): 2 (March)
    Pages: 223-229

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    Handle: RePEc:eee:mateco:v:46:y:2010:i:2:p:223-229
    Contact details of provider: Web page: http://www.elsevier.com/locate/jmateco

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    1. 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..
    2. Heifetz, Aviad & Mongin, Philippe, 2001. "Probability Logic for Type Spaces," Games and Economic Behavior, Elsevier, vol. 35(1-2), pages 31-53, April.
    3. Heifetz, Aviad & Samet, Dov, 1998. "Topology-Free Typology of Beliefs," Journal of Economic Theory, Elsevier, vol. 82(2), pages 324-341, October.
    4. MEIER, Martin, 2001. "An infinitary probability logic for type spaces," CORE Discussion Papers 2001061, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Miklós Pintér, 2005. "Type space on a purely measurable parameter space," Economic Theory, Springer, vol. 26(1), pages 129-139, 07.
    6. Heifetz, Aviad & Samet, Dov, 1999. "Coherent beliefs are not always types," Journal of Mathematical Economics, Elsevier, vol. 32(4), pages 475-488, December.
    7. Robert J. Aumann, 1999. "Interactive epistemology II: Probability," International Journal of Game Theory, Springer, vol. 28(3), pages 301-314.
    8. MERTENS , Jean-François & SORIN , Sylvain & ZAMIR , Shmuel, 1994. "Repeated Games. Part B : The Central Results," CORE Discussion Papers 1994021, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. MERTENS , Jean-François & SORIN , Sylvain & ZAMIR , Shmuel, 1994. "Repeated Games. Part A : Background Material," CORE Discussion Papers 1994020, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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