Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/150143
Authors: 
Xiong, Siyang
Chen, Yi-Chun
di Tillio, Alfredo
Faingold, Eduardo
Year of Publication: 
2010
Citation: 
[Journal:] Theoretical Economics [ISSN:] 1555-7561 [Volume:] 5 [Year:] 2010 [Issue:] 3 [Pages:] 445-478
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.
Subjects: 
Rationalizability
incomplete information
higher-order beliefs
strategic topology
electronic mail game
JEL: 
C70
Persistent Identifier of the first edition: 
Creative Commons License: 
https://creativecommons.org/licenses/by-nc/3.0/
Document Type: 
Article

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