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Bounded Rationality and Correlated Equilibria

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  • Germano, Fabrizio
  • Zuazo-Garin, Peio

Abstract

We study an interactive framework that explicitly allows for nonrational behavior. We do not place any restrictions on how players' behavior deviates from rationality. Instead we assume that there exists a probability p such that all players play rationally with at least probability p, and all players believe, with at least probability p, that their opponents play rationally. This, together with the assumption of a common prior, leads to what we call the set of p-rational outcomes, which we define and characterize for arbitrary probability p. We then show that this set varies continuously in p and converges to the set of correlated equilibria as p approaches 1, thus establishing robustness of the correlated equilibrium concept to relaxing rationality and common knowledge of rationality. The p-rational outcomes are easy to compute, also for games of incomplete information, and they can be applied to observed frequencies of play to derive a measure p that bounds from below the probability with which any given player chooses actions consistent with payoff maximization and common knowledge of payoff maximization. Keywords: strategic interaction, correlated equilibrium, robustness to bounded rationality, approximate knowledge, incomplete information, measure of rationality, experiments. JEL Classification: C72, D82, D83.

Suggested Citation

  • Germano, Fabrizio & Zuazo-Garin, Peio, 2015. "Bounded Rationality and Correlated Equilibria," Working Papers 2072/260959, Universitat Rovira i Virgili, Department of Economics.
    • Handle: RePEc:urv:wpaper:2072/260959
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    Cited by:

    1. Germano, Fabrizio & Weinstein, Jonathan & Zuazo-Garin, Peio, 2020. "Uncertain rationality, depth of reasoning and robustness in games with incomplete information," Theoretical Economics, Econometric Society, vol. 15(1), January.
    2. Ziegler, Gabriel, 2022. "Informational robustness of common belief in rationality," Games and Economic Behavior, Elsevier, vol. 132(C), pages 592-597.
    3. Gabriel Ziegler, 2021. "Informational Robustness of Common Belief in Rationality," Papers 2103.02402, arXiv.org, revised Feb 2022.

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    Keywords

    Jocs no-cooperatius (Matemàtica); Teoria de la informació (Economia); 33 - Economia;
    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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