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Approximate Knowledge of Rationality and Correlated Equilibria

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  • Fabrizio Germano
  • Peio Zuazo-Garin

Abstract

We extend Aumann's theorem [Aumann 1987], 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 probability p or more. We show that behavior in this case constitutes a kind 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.

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Bibliographic Info

Paper provided by Barcelona Graduate School of Economics in its series Working Papers with number 642.

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Date of creation: Jun 2012
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Handle: RePEc:bge:wpaper:642

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Keywords: correlated equilibrium; approximate common knowledge; bounded rationality; p-rational belief system; common prior; information; noncooperative game;

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  1. Sergiu Hart, 2004. "Adaptive Heuristics," Discussion Paper Series dp372, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  2. T. Börgers, 2010. "Weak Dominance and Approximate Common Knowledge," Levine's Working Paper Archive 378, David K. Levine.
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