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

Listed author(s):
  • Martin Hellwig

    ()

    (Max Planck Institute for Research on Collective Goods)

Kolmogorov’s extension theorem provides a natural mapping from the space of coherent hierarchies of an agent’s first-order, second-order, etc. beliefs to the space of probability measures over the exogenous parameters and the other agents' belief hierarchies. Mertens and Zamir (1985) showed that, if the spaces of belief hierarchies are endowed with the product topology, then this mapping is a homeomorphism. This paper shows that this mapping is also a homeomorphism if the spaces of belief hierarchies are endowed with the uniform weak topology of Chen et al. (2010) or the universal strategic topology of Dekel et al. (2006), both of which ensure that strategic behaviour exhibits desirable continuity properties.

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File URL: http://www.coll.mpg.de/pdf_dat/2016_17online.pdf
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Paper provided by Max Planck Institute for Research on Collective Goods in its series Discussion Paper Series of the Max Planck Institute for Research on Collective Goods with number 2016_17.

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Date of creation: Nov 2016
Handle: RePEc:mpg:wpaper:2016_17
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  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.
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