Uniform Topologies on Types
Uniform Topologies on Types
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类型上的统一拓扑
DOI：
10.2139/ssrn.1494432
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
Siyang Xiong
中科院分区：
文献类型：
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作者：
Yi;A. Di Tillio;E. Faingold;Siyang Xiong
我们研究了临时相关合理化对高阶信念扰动的稳健性。我们在普适类型空间上引入了一种新的度量拓扑，称为一致弱拓扑，在这种拓扑下，如果两种类型具有相似的一阶信念，则它们是接近的，并将相似的概率附加到具有相似一阶信念的其他参与者，等等，其中相似程度在信念层次上是一致的。这种拓扑结构基于共同的p-信念推广了现在经典的接近共同知识的概念(Monderer和Samet())。我们证明了一致弱拓扑中的收敛蕴含着一致策略拓扑中的收敛(Dekel，Fudenberg和Morris(2006))。此外，当极限是有限类型时，一致弱收敛也是策略拓扑收敛的必要条件。最后，我们证明了有限类型集在一致策略拓扑下是无处稠密的。因此，我们的结果揭示了游戏中信念相似和行为相似之间的联系。
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.