Please use this identifier to cite or link to this item: https://repositorio.insper.edu.br/handle/11224/4878
Type: Artigo Científico
Title: Uniform topologies on types
Author: Chen, Yi-Chun
Di Tillio, Alfredo
Faingold, Eduardo
Xiong, Siyang
Publication Date: 2010
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 (english terms): Rationalizability
Incomplete information
Higher-order beliefs
Strategic topology
Electronic mail game
Language: Inglês
CNPq Area: Ciências Sociais Aplicadas
URI: https://econtheory.org/ojs/index.php/te/article/viewArticle/20100445
Copyright: O INSPER E ESTE REPOSITÓRIO NÃO DETÊM OS DIREITOS DE USO E REPRODUÇÃO DOS CONTEÚDOS AQUI REGISTRADOS. É RESPONSABILIDADE DOS USUÁRIOS INDIVIDUAIS VERIFICAR OS USOS PERMITIDOS NA FONTE ORIGINAL, RESPEITANDO-SE OS DIREITOS DE AUTOR OU EDITOR
Notes: Texto completo
Appears in Collections:Coleção de Artigos Científicos

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