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Full-Text Articles in Social and Behavioral Sciences
Uniform Topologies On Types, Yi-Chun Chen, Alfredo Di Tillio, Eduardo Faingold, Siyang Xiong
Uniform Topologies On Types, Yi-Chun Chen, Alfredo Di Tillio, Eduardo Faingold, Siyang Xiong
Cowles Foundation Discussion Papers
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 …
Rationalizable Implementation, Dirk Bergemann, Stephen Morris
Rationalizable Implementation, Dirk Bergemann, Stephen Morris
Cowles Foundation Discussion Papers
This note studies (full) implementation of social choice functions under complete information in (correlated) rationalizable strategies. The monotonicity condition shown by Maskin (1999) to be necessary for Nash implementation is also necessary under the more stringent solution concept. We show that it is also sufficient under a mild “no worst alternative” condition. In particular, no economic condition is required.
Rationalizable Implementation, Dirk Bergemann, Stephen Morris, Olivier Tercieux
Rationalizable Implementation, Dirk Bergemann, Stephen Morris, Olivier Tercieux
Cowles Foundation Discussion Papers
We consider the implementation of social choice functions under complete information in rationalizable strategies. A strict (and thus stronger) version of the monotonicity condition introduced by Maskin (1999) is necessary under the solution concept of rationalizability. Assuming the social choice function is responsive (i.e., it never selects the same outcome in two distinct states), we show that it is also sufficient under a mild “no worst alternative” condition. In particular, no economic condition is required. We also discuss how our results extend when the social choice function is not responsive.