Full Implementation via Information Design in Nonatomic Games

This paper studies the implementation of Bayes correlated equilibria in symmetric Bayesian nonatomic games, using direct information structures and obedient strategies. The main results demonstrate full implementation in a class of games with positive cost externalities. Specifically, if the game admits a strictly convex 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 only weakly convex, we show that all equilibria implement the same expected social cost. Additionally, all Bayes correlated equilibria, including those with infinite support or irrational action distributions, are approximately implemented.