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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.

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Bibliographic Info

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

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Web page: http://www.elsevier.com/locate/jmateco

Related research

Keywords: Harsanyi program Type space Hierarchy of beliefs Games with incomplete information;

References

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  1. 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).
  2. Miklós Pintér, 2005. "Type space on a purely measurable parameter space," Economic Theory, Springer, vol. 26(1), pages 129-139, 07.
  3. 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).
  4. A. Heifetz & Ph. Mongin, 1998. "Probability logic for type spaces," THEMA Working Papers 98-25, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  5. 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).
  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. Aviad Heifetz & Dov Samet, 1996. "Topology-Free Typology of Beliefs," Game Theory and Information 9609002, EconWPA, revised 17 Sep 1996.
  8. Brandenburger Adam & Dekel Eddie, 1993. "Hierarchies of Beliefs and Common Knowledge," Journal of Economic Theory, Elsevier, vol. 59(1), pages 189-198, February.
  9. Robert J. Aumann, 1999. "Interactive epistemology II: Probability," International Journal of Game Theory, Springer, vol. 28(3), pages 301-314.
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Citations

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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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