Uniform Topology on Types and Strategic Convergence


Abstract: We study the continuity of the correspondence of interim epsilon-rationalizable actions in incomplete information games. We introduce a topology on types, called uniform weak topology, under which two types of a player 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 notion of proximity of types is an extension of the concept of common p-belief due to Monderer and Samet (1989). We show that given any finite game every action that is interim rationalizable for a finite type t remains interim epsilon-rationalizable for all types sufficiently close to t in the uniform-weak topology. Conversely, given any finite type t there exist epsilon > 0 and a finite game such that some interim rationalizable action for t fails to be interim epsilon-rationalizable for every type that is not close to t in the uniform-weak topology. Our results thus establish the equivalence between the uniform-weak topology and the strategic topology of Dekel, Fudenberg, and Morris (2006) around finite types.
This is joint work with Alfredo Di Tillio (Universita Luigi Bocconi).

Biography:  Eduardo Faingold received a M.Sc. in Mathematics from the Instituto de Matematica Pura e Aplicada (IMPA) in Rio de Janeiro in 2000 and a Ph.D. in Economics from the University of Pennsylvania in 2006.  He joined the department of economics at Yale University as an assistant professor in 2006. His research interests include the study of reputation effects and incomplete information in repeated games, dynamic games played in continuous time and the Bayesian foundation of incomplete information games.


Eduardo Faingold