Improving Nash by coarse correlation

We consider a class of symmetric two-person quadratic games where coarse correlated equilibria — CCE — (Moulin and Vial 1978) can strictly improve upon the Nash equilibrium payoffs, while correlated equilibrium — CE — (Aumann 1974, 1987) cannot, because these games are potential games. We compute the largest feasible total utility in any CCE in those games, and show that it is achieved by a CCE involving only two pure strategy profiles. Applications include the Cournot duopoly and the game of public good provision, where the improvement over and above the Nash equilibrium payoff can be sustantial.