Ulric B. and Evelyn L. Bray Social Sciences Seminar

Abstract: Correlated equilibria emerge naturally when agents communicate prior to interactions or rely on intermediaries such as recommendation systems. We study when a given Nash equilibrium can be improved within the set of correlated equilibria with respect to general objectives. Our key insight is a detail-free criterion linking improvability with the extent of randomization: a Nash equilibrium with three or more randomizing agents is necessarily non-extreme within the set of correlated equilibria and is thus improvable for any generic social objective. We refine this insight in applications to specific classes of games and objectives, including Pareto and utilitarian welfare, and show how to construct improving correlated equilibria. Our findings underscore the ubiquity of improvable Nash equilibria and indicate the crucial role of correlated strategies in enhancing strategic outcomes.

Joint work with Kirill Rudov and Fedor Sandomirskiy