# Topologies on Types

 Title: Topologies on Types Author: Morris, Stephen; Dekel, Eddie; Fudenberg, Drew Note: Order does not necessarily reflect citation order of authors. Citation: Dekel, Eddie, Drew Fudenberg, and Stephen Morris. 2006. Topologies on types. Theoretical Economics 1, no. 3: 275–309. Full Text & Related Files: fudenberg_topologies.PDF (348.5Kb; PDF) Abstract: 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. Published Version: http://econtheory.org Other Sources: http://econtheory.org/ojs/index.php/te/article/view/20060275 Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:3160489 Downloads of this work:

Advanced Search