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T-Space at The University of Toronto Libraries >
Theoretical Economics >
Volume 5, Number 3 (September 2010) >

Please use this identifier to cite or link to this item: http://hdl.handle.net/1807/27192

Title: Uniform topologies on types
Authors: Yi-Chun Chen; Department of Economics, National University of Singapore
Alfredo di Tillio; Department of Economics, Università Luigi Bocconi
Eduardo Faingold; Department of Economics, Yale University
Siyang Xiong; Department of Economics, Rice University
Keywords: Rationalizability, incomplete information, higher-order beliefs, strategic topology, electronic mail game
C70
Issue Date: 22-Sep-2010
Publisher: Theoretical Economics
Citation: Theoretical Economics; Vol 5, No 3 (2010)
Abstract: [This item is a preserved copy. To view the original, visit http://econtheory.org/] 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.
URI: http://hdl.handle.net/1807/27192
Other Identifiers: http://econtheory.org/ojs/index.php/te/article/view/20100445
Rights: Authors who publish in <i>Theoretical Economics</i> will release their articles under the <a href="http://creativecommons.org/licenses/by-nc/2.5/">Creative Commons Attribution-NonCommercial license</a>. This license allows anyone to copy and distribute the article for non-commercial purposes provided that appropriate attribution is given.
Appears in Collections:Volume 5, Number 3 (September 2010)

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