Bounded rationality and correlated equilibria

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: strategic interaction, correlated equilibrium, robustness to bounded rationality, approximate knowledge, incomplete information, measure of rationality, experiments. JEL Classification: C72, D82, D83.

Uncertain rationality, depth of reasoning and robustness in games with incomplete information

“… A related result by Germano and Zuazo‐Garin () shows that their notion of p‐rational outcomes (which coincide with the correlated equilibria when and otherwise generalize these by assuming common knowledge of mutual p ‐belief in rationality rather than common knowledge of rationality) are continuous in p , for any , which, in particular, implies robustness of correlated equilibria to bounded rationality. …”

Informational Robustness of Common Belief in Rationality

“…2 Some of these ideas are fruitfully applied to the theory of robust mechanism design as initiated by Bergemann and Morris (2005, 2009. Other papers dealing with related ideas about robustness include Battigalli (1999Battigalli ( , 2003, Battigalli and Siniscalchi (2003), Dekel et al (2007), Liu (2015), Tang (2015), and Germano and Zuazo-Garin (2017). player i there is (i) a finite set of (pure) actions A i , (ii) a finite set of payoff types, 4 and (iii) a utility function u i : A × Θ → R, where A := i∈I A i and Θ := i∈I∪{0} Θ i denote the set of action profiles and payoff states, respectively.…”