# Bounded Rationality and Correlated Equilibria

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

Working Papers from HAL

**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:** incomplete information; approximate knowledge; strategic interaction; correlated equilibrium; robustness to bounded rationality; experiments; measure of rationality (search for similar items in EconPapers)

**New Economics Papers:** this item is included in nep-cbe, nep-evo, nep-gth, nep-hpe, nep-mic and nep-upt

**Date:** 2015-11

**Note:** View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-01251512

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**Related works:**

Journal Article: Bounded rationality and correlated equilibria (2017)

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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