Information Design and Full Implementation in Nonatomic Games

TL;DR

This paper explores how to implement Bayesian correlated equilibria in symmetric nonatomic games using direct information structures, demonstrating full implementation in certain classes of games with externalities and potential functions.

Contribution

It introduces conditions under which Bayes correlated equilibria can be fully implemented in nonatomic games with negative externalities, expanding the understanding of information design in such settings.

Findings

Full implementation for games with strictly concave potential functions.

Equilibrium outcomes with weakly concave potential have consistent expected payoffs.

Approximate implementation extends to equilibria with infinite support or irrational actions.

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.