Yi-Chun Chen (Dept. of Economics, National University of Singapore) Alfredo Di Tillio (IGIR and Dept. of Economics, Universita Luigi Bocconi) Eduardo Faingold () (Cowles Foundation, Yale University) Siyang Xiong (Dept. of Economics, Rice University)
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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.
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Find related papers by JEL classification: C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
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Dekel, Eddie & Fudenberg, Drew & Morris, Stephen, 2006.
"Topologies on types,"
Theoretical Economics,
Society for Economic Theory, vol. 1(3), pages 275-309, September.
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Other versions:
Eddie Dekel & Drew Fudenberg, 2006.
"Topologies on Type,"
Discussion Papers
1417, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
[Downloadable!]
Eddie Dekel & Drew Fudenberg & Stephen Morris, 2005.
"Topologies on Types,"
Levine's Bibliography
784828000000000061, UCLA Department of Economics.
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