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 Please use this identifier to cite or link to this item: http://hdl.handle.net/1807/9415

 Title: Topologies on types Authors: Eddie Dekel; Northwestern University and Tel Aviv UniversityDrew Fudenberg; Harvard UniversityStephen Morris; Princeton University Keywords: Rationalizability, incomplete information, common knowledge, universal type space, strategic topologyC70, C72 Issue Date: 7-Sep-2006 Publisher: Theoretical Economics Citation: Theoretical Economics; Vol 1, No 3 (2006); 275-309 Abstract: [This item is a preserved copy. To view the original, visit http://econtheory.org/] We define and analyze a "strategic topology'' on types in the Harsanyi-Mertens-Zamir universal type space, where two types are close if their strategic behavior is similar in all strategic situations. For a fixed game and action define the distance between a pair of types as the difference between the smallest epsilon for which the action is epsilon interim correlated rationalizable. We define a strategic topology in which a sequence of types converges if and only if this distance tends to zero for any action and game. Thus a sequence of types converges in the strategic topology if that smallest epsilon does not jump either up or down in the limit. As applied to sequences, the upper-semicontinuity property is equivalent to convergence in the product topology, but the lower-semicontinuity property is a strictly stronger requirement, as shown by the electronic mail game. In the strategic topology, the set of "finite types'' (types describable by finite type spaces) is dense but the set of finite common-prior types is not. URI: http://hdl.handle.net/1807/9415 Other Identifiers: http://econtheory.org/ojs/index.php/te/article/view/20060275 Rights: Authors who publish in Theoretical Economics will release their articles under the Creative Commons Attribution-NonCommercial license. This license allows anyone to copy and distribute the article for non-commercial purposes provided that appropriate attribution is given. Appears in Collections: Volume 1, Number 3 (September 2006)

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