Uniform topologies on types

, (), , (), , () and , ()
Additional contact information
,: Department of Economics, National University of Singapore
,: Department of Economics, Università Luigi Bocconi
,: Department of Economics, Yale University
,: Department of Economics, Rice University
Authors registered in the RePEc Author Service: Yi-Chun Chen (), Alfredo Di Tillio () and Siyang Xiong

Theoretical Economics, 2010, vol. 5, issue 3

Abstract: We study the robustness of interim correlated rationalizability to perturbations of higher-order beliefs. We introduce a new metric topology on the universal type space, called uniform weak topology, under which two types are close if they have similar first-order beliefs, attach similar probabilities to other players having similar first-order beliefs, and so on, where the degree of similarity is uniform over the levels of the belief hierarchy. This topology generalizes the now classic notion of proximity to common knowledge based on common p-beliefs (Monderer and Samet 1989). We show that convergence in the uniform weak topology implies convergence in the uniform strategic topology (Dekel, Fudenberg, and Morris 2006). Moreover, when the limit is a finite type, uniform-weak convergence is also a necessary condition for convergence in the strategic topology. Finally, we show that the set of finite types is nowhere dense under the uniform strategic topology. Thus, our results shed light on the connection between similarity of beliefs and similarity of behaviors in games.

Keywords: Rationalizability; incomplete information; higher-order beliefs; strategic topology; electronic mail game (search for similar items in EconPapers)
JEL-codes: C70 (search for similar items in EconPapers)
Date: 2010-09-22
References: Add references at CitEc
Citations: View citations in EconPapers (23)

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Working Paper: Uniform Topologies on Types (2009)
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