HEC Research Papers Series,
HEC Paris

Abstract: This paper studies the implementation of Bayes correlated equilibria in symmetric Bayesian games with nonatomic players, using direct information structures and obedient strategies. The main results demonstrate full implementation in a class of games with negative payoff externalities, such as congestion and Cournot games. Specifically, if the game admits a strictly concave potential in every state, then for every Bayes correlated equilibrium outcome with finite support and rational action distributions, there exists a direct information structure that implements this outcome under all equilibria. When the potential is weakly concave, we show that all equilibria implement the same expected total payoff. Additionally, all Bayes correlated equilibria, including those with infinite support or irrational action distributions, are approximately implemented.

Keywords: Bayes correlated equilibrium; congestion games; aggregative games; information design; population games; potential games.

JEL-codes: C72; D62; D82

21 pages, February 27, 2026

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