Approximate knowledge of rationality and correlated equilibria

Fabrizio Germano and Peio Zuazo-Garin

Economics Working Papers from Department of Economics and Business, Universitat Pompeu Fabra

Abstract: We extend Aumann's [3] theorem, deriving correlated equilibria as a consequence of common priors and common knowledge of rationality, by explicitly allowing for non-rational behavior. We replace the assumption of common knowledge of rationality with a substantially weaker one, joint p-belief of rationality, where agents believe the other agents are rational with probabilities p = (pi)i?I or more. We show that behavior in this case constitutes a type of correlated equilibrium satisfying certain p-belief constraints, and that it varies continuously in the parameters p and, for p sufficiently close to one, with high probability is supported on strategies that survive the iterated elimination of strictly dominated strategies. Finally, we extend the analysis to characterizing rational expectations of interim types, to games of incomplete information, as well as to the case of non-common priors.

Keywords: Approximate common knowledge; bounded rationality; p-rational belief system; correlated equilibrium; incomplete information; non-cooperative game. (search for similar items in EconPapers)
JEL-codes: C72 D82 D83 (search for similar items in EconPapers)
Date: 2012-06, Revised 2012-10
New Economics Papers: this item is included in nep-gth, nep-knm and nep-upt
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Related works:
Working Paper: Approximate Knowledge of Rationality and Correlated Equilibria (2015)
Working Paper: Approximate Knowledge of Rationality and Correlated Equilibria (2012)
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