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A Homeomorphism Theorem for the Universal Type Space with the Uniform Topology

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  • Martin Hellwig

    () (Max Planck Institute for Research on Collective Goods)

Abstract

The paper proves a homeomorphism theorem for the universal type space with the uniform strategic topology or the uniform weak topology that Dekel et al. (2006) and Chen et al. (2010) introduced in order to take account of the fact that beliefs of arbitrarily high orders in agents' belief hierarchies can have a signi cant impact on strategic behaviour. Probability measures on the larger σ-algebras associated with these finer topologies are the completions of probability measures on the product σ-algebras, Kolmogorov's extension theorem can still be used to derive probability measures from belief hierarchies. The extended Kolmogorov mapping that is thus obtained is a homeomorphism.

Suggested Citation

  • Martin Hellwig, 2016. "A Homeomorphism Theorem for the Universal Type Space with the Uniform Topology," Discussion Paper Series of the Max Planck Institute for Research on Collective Goods 2016_17, Max Planck Institute for Research on Collective Goods, revised May 2017.
  • Handle: RePEc:mpg:wpaper:2016_17
    as

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    File URL: http://www.coll.mpg.de/pdf_dat/2016_17online.pdf
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    References listed on IDEAS

    as
    1. Heifetz, Aviad & Samet, Dov, 1998. "Topology-Free Typology of Beliefs," Journal of Economic Theory, Elsevier, vol. 82(2), pages 324-341, October.
    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. Yi-Chun Chen & Alfredo Di Tillio & Eduardo Faingold & Siyang Xiong, 2012. "The Strategic Impact of Higher-Order Beliefs," Cowles Foundation Discussion Papers 1875, Cowles Foundation for Research in Economics, Yale University.
    4. Rubinstein, Ariel, 1989. "The Electronic Mail Game: Strategic Behavior under "Almost Common Knowledge."," American Economic Review, American Economic Association, vol. 79(3), pages 385-391, June.
    5. Heifetz, Aviad, 1993. "The Bayesian Formulation of Incomplete Information--The Non-compact Case," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(4), pages 329-338.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    incomplete information; universal type space; uniform weak topology; uniform strategic topology; homeomorphism theorem;

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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