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Approximate knowledge of rationality and correlated equilibria

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  • Fabrizio, Germano
  • Zuazo Garín, Peio

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 notion, joint p-belief of rationality, where agents believe the other agents are rational with probabilities p = (pi)i2I 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 su ciently 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 [4] theorem on rational expectations of interim types to the broader p-rational belief systems, and also discuss the case of non-common priors.

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Paper provided by Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I in its series IKERLANAK with number Ikerlanak;2012-61.

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Date of creation: 16 Jul 2012
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Handle: RePEc:ehu:ikerla:8757

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Postal: Dpto. de Fundamentos del Análisis Económico I, Facultad de CC. Económicas y Empresariales, Universidad del País Vasco, Avda. Lehendakari Aguirre 83, 48015 Bilbao, Spain
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Keywords: bounded rationality; correlated equilibrium; aproximate common knowledge; p-rational blief system; common prior; information noncooperative game;

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  1. T. Börgers, 2010. "Weak Dominance and Approximate Common Knowledge," Levine's Working Paper Archive 378, David K. Levine.
  2. Sergiu Hart, 2004. "Adaptive Heuristics," Levine's Bibliography 122247000000000471, UCLA Department of Economics.
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