Extreme Equilibria: The Benefits of Correlation
For game theorists and economists, it provides a general criterion for when correlation can improve strategic outcomes, with implications for mechanism design and multi-agent systems.
The paper shows that any Nash equilibrium with three or more randomizing agents can generically be improved upon by a correlated equilibrium, demonstrating the ubiquity of improvable Nash equilibria and the benefits of correlation.
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.