# Bounded rationality and correlated equilibria

*Fabrizio Germano* () and
*Peio Zuazo-Garin* ()

*International Journal of Game Theory*, 2017, vol. 46, issue 3, 595-629

**Abstract:**
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, but rather, on players’ higher-order beliefs about the frequency of such deviations. We assume that there exists a probability p such that 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. Importantly, they can be applied to observed frequencies of play for arbitrary normal-form games to derive a measure of rationality $$\overline{p}$$ 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 (search for similar items in EconPapers)

**JEL-codes:** C72 D82 D83 (search for similar items in EconPapers)

**Date:** 2017

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**Related works:**

Working Paper: Bounded Rationality and Correlated Equilibria (2015)

Working Paper: Bounded Rationality and Correlated Equilibria (2015)

Working Paper: Bounded Rationality and Correlated Equilibria (2015)

Working Paper: Bounded rationality and correlated equilibria (2015)

Working Paper: Bounded Rationality and Correlated Equilibria (2015)

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