Coarse correlated equilibria in an abatement game

We consider the well-analyzed abatement game (Barrett 1994) and prove that correlation among the players (nations) can strictly improve upon the Nash equilibrium payoffs. As these games are potential games, correlated equilibrium — CE — (Aumann 1974, 1987) cannot improve upon Nash; however we prove that coarse correlated equilibria — CCE — (Moulin and Vial 1978) may do so. We compute the largest feasible total utility and hence the efficiency gain in any CCE in those games: it is achieved by a lottery over only two pure strategy profiles.