Bounded Rationality and Correlated Equilibria

• Authors: Fabrizio Germano.
• BSE Working Paper: 110293 | September 15
• Keywords: experiments , Incomplete Information , correlated equilibrium , strategic interaction , robustness to bounded rationality , approximate knowledge , measure of rationality
• JEL codes: C72, D82, D83
• experiments
• Incomplete Information
• correlated equilibrium
• strategic interaction
• robustness to bounded rationality
• approximate knowledge
• measure of rationality

We study an interactive framework that explicitly allows for non-rational behavior. We do not place any restrictions on how players can deviate from rational behavior. Instead we assume that there exists a lower bound p 2 [0; 1] such that all players play and are believed to play rationally with a probability p or more. 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 p 2 [0; 1]. 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 compute a measure p that bounds from below the probability with which any given player is choosing actions consistent with payoff maximization and common knowledge of payoff maximization.