Bounded rationality and correlated equilibria |
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Authors: | Fabrizio Germano Peio Zuazo-Garin |
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Institution: | 1.Departament d’Economia i Empresa, and Barcelona GSE,Universitat Pompeu Fabra,Barcelona,Spain;2.Department of Foundations of Economic Analysis I, BRiDGE Group,University of the Basque Country (UPV/EHU),Bilbao,Spain |
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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 \(\overline{p}\) that bounds from below the probability with which any given player chooses actions consistent with payoff maximization and common knowledge of payoff maximization. |
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