International Journal of Game Theory (forthcoming)

**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 ameasure of rationality *p* that bounds from below the probability with which any given player chooses actions consistent with payoff maximization and common knowledgeof payoff maximization.

bridge | Faculty of Economics. University of the Basque Country UPV/EHU Página web creada por alalpe.es