Please use this identifier to cite or link to this item: https://doi.org/10.3982/TE462
Title: Uniform topologies on types
Authors: Chen, Y.-C. 
Di Tillio, A.
Faingold, E.
Xiong, S.
Keywords: Electronic Mail game
Higher-order beliefs
Incomplete information
Rationalizability
Strategic topology
Issue Date: Sep-2010
Source: Chen, Y.-C., Di Tillio, A., Faingold, E., Xiong, S. (2010-09). Uniform topologies on types. Theoretical Economics 5 (3) : 445-478. ScholarBank@NUS Repository. https://doi.org/10.3982/TE462
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 et al. 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. Copyright © 2010 Yi-Chun Chen, Alfredo Di Tillio, Eduardo Faingold, and Siyang Xiong.
Source Title: Theoretical Economics
URI: http://scholarbank.nus.edu.sg/handle/10635/52136
ISSN: 19336837
DOI: 10.3982/TE462
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