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

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Hellwig,  Martin
Max Planck Institute for Research on Collective Goods, Max Planck Society;

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http://www.coll.mpg.de/pdf_dat/2016_17online.pdf
(Preprint)

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Citation

Hellwig, M. (2016). A Homeomorphism Theorem for the Universal Type Space with the Uniform Topology.


Cite as: https://hdl.handle.net/11858/00-001M-0000-002B-BC8A-A
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 significant 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.