Extreme Equilibria: The Benefits of Correlation
Kirill Rudov, Fedor Sandomirskiy, Leeat Yariv
TLDR
This paper shows that Nash equilibria with three or more randomizing agents can almost always be improved using correlated strategies.
Key contributions
- Introduces a detail-free criterion for improving Nash equilibria.
- Shows Nash equilibria with 3+ randomizing agents are generically improvable.
- Provides constructive methods to improve outcomes in specific game classes.
- Highlights the widespread potential for correlation to enhance strategic results.
Why it matters
This research reveals that many Nash equilibria can be improved through correlation, especially in games with multiple randomizing agents. It provides practical methods to achieve better outcomes, emphasizing the critical role of communication and intermediaries in strategic interactions.
Original 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.
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