Approximate Knowledge of Rationality and Correlated Equilibria

Fabrizio Germano and Peio Zuazo-Garin

Discussion Paper Series from The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem

Abstract: We extend Aumann's theorem (Aumann, 1987) in 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 notion, p-belief of rationality, where agents believe the other agents are rational with probabilities p or more. We show that behavior in this case constitutes a constrained correlated equilibrium of a doubled game satisfying certain p-belief constraints and characterize the topological structure of the resulting set of p-rational outcomes. We establish continuity in the parameters p and show that, for p sufficiently close to one, the p-rational outcomes are close to the correlated equilibria and, with high probability, supported on strategies that survive the iterated elimination of strictly dominated strategies. Finally, we extend Aumann and Dreze's theorem (Aumann and Dreze, 2008) on rational expectations of interim types to the broader p-rational belief systems, and also discuss the case of non-common priors.

Keywords: Correlated equilibrium; approximate common knowledge; bounded rationality; p-rational belief system; common prior; information; noncooperative game (search for similar items in EconPapers)
JEL-codes: C72 D82 D83 (search for similar items in EconPapers)
Pages: 20 pages
Date: 2012-06
New Economics Papers: this item is included in nep-gth, nep-knm, nep-mic 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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