Bounded rationality and correlated equilibria

Germano, Fabrizio; Zuazo-Garin, Peio

doi:http://dx.doi.org/10.1007/s00182-016-0547-5

Bounded rationality and correlated equilibria

Citation

Germano F, Zuazo-Garin P. Bounded rationality and correlated equilibria. Int J Game Theory. 2017 Aug;46(3):595-629. DOI: 10.1007/s00182-016-0547-5

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