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Approximate knowledge of rationality and correlated equilibria

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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.

Suggested Citation

  • Fabrizio Germano & Peio Zuazo-Garin, 2012. "Approximate knowledge of rationality and correlated equilibria," Economics Working Papers 1326, Department of Economics and Business, Universitat Pompeu Fabra, revised Oct 2012.
    • Handle: RePEc:upf:upfgen:1326
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    References listed on IDEAS

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    1. Borgers Tilman, 1994. "Weak Dominance and Approximate Common Knowledge," Journal of Economic Theory, Elsevier, vol. 64(1), pages 265-276, October.
    2. Hu, Tai-Wei, 2007. "On p-rationalizability and approximate common certainty of rationality," Journal of Economic Theory, Elsevier, vol. 136(1), pages 379-391, September.
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    More about this item

    Keywords

    Approximate common knowledge; bounded rationality; p-rational belief system; correlated equilibrium; incomplete information; non-cooperative game.;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness

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