Correlated Equilibria in Large Anonymous Bayesian Games

Frederic Koessler, Marco Scarsini () and Tristan Tomala ()
Additional contact information
Marco Scarsini: Luiss University, 00197 Rome, Italy
Tristan Tomala: Groupement de Recherche et d’Etudes en Gestion à HEC Paris, National Center for Scientific Research, 78351 Jouy-en-Josas, France

Mathematics of Operations Research, 2025, vol. 50, issue 3, 2157-2174

Abstract: We consider multipopulation Bayesian games with a large number of players. Each player aims at minimizing a cost function that depends on this player’s own action, the distribution of players’ actions in all populations, and an unknown state parameter. We study the nonatomic limit versions of these games and introduce the concept of Bayes correlated Wardrop equilibrium, which extends the concept of Bayes correlated equilibrium to nonatomic games. We prove that Bayes correlated Wardrop equilibria are limits of action flows induced by Bayes correlated equilibria of the game with a large finite set of small players. For nonatomic games with complete information admitting a convex potential, we prove that the set of correlated and of coarse correlated Wardrop equilibria coincide with the set of probability distributions over Wardrop equilibria and that all equilibrium outcomes have the same costs. We get the following consequences. First, all flow distributions of (coarse) correlated equilibria in convex potential games with finitely many players converge to mixtures of Wardrop equilibria when the weight of each player tends to zero. Second, for any sequence of flows satisfying a no-regret property, its empirical distribution converges to the set of distributions over Wardrop equilibria, and the average cost converges to the unique Wardrop cost.

Keywords: Primary: 91A07; 91A14; 91A27; secondary: 91A26; Bayes correlated equilibrium; coarse correlated equilibrium; congestion games; no regret; nonatomic games; potential games; selfish routing; Wardrop equilibrium (search for similar items in EconPapers)
Date: 2025
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http://dx.doi.org/10.1287/moor.2023.0278 (application/pdf)

Related works:
Working Paper: Correlated Equilibria in Large Anonymous Bayesian Games (2023)
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:50:y:2025:i:3:p:2157-2174

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