Extreme Equilibria: The Benefits of Correlation

TL;DR

This paper investigates how correlated equilibria can improve upon Nash equilibria in multi-agent games, highlighting the widespread potential for enhancement through correlation.

Contribution

It introduces a detail-free criterion for when Nash equilibria are improvable via correlation, applicable to various game classes and objectives.

Findings

Any Nash equilibrium with three or more randomizing agents is generically improvable.

Constructive methods are provided to improve equilibria under different objectives.

Correlation plays a crucial role in enhancing strategic outcomes.

Abstract

Correlated equilibria arise naturally when agents communicate or rely on intermediaries such as recommendation systems. We study when a given Nash equilibrium can be improved within the set of correlated equilibria for general objectives. Our key insight is a detail-free criterion: any Nash equilibrium with three or more randomizing agents is generically improvable. We refine this insight to specific classes of games and objectives, including Pareto and utilitarian welfare, and provide constructive methods to obtain improvements. Our findings underscore the ubiquity of improvable Nash equilibria and the crucial role of correlation in enhancing strategic outcomes.