The Irreversible Pollution Game

We study a 2-country differential game with irreversible pollution. Irreversibility is of a hard type: above a certain threshold level of pollution, the self-cleaning capacity of Nature drops to zero. Accordingly, the game includes a non-concave feature, and we characterize both the cooperative and non-cooperative versions with this general non-LQ property. We deliver full analytical results for the existence of Markov Perfect Equilibria. We first demonstrate that when pollution costs are equal across players (symmetry), irreversible pollution regimes are more frequently reached than under cooperation. Second, we study the implications of asymmetry in the pollution cost. We find far nontrivial results on the reachability of the irreversible regime. However, we unambiguously prove that, for the same total cost of pollution, provided the irreversible regime is reached in both the symmetric and asymmetric cases, long-term pollution is larger in the symmetric case, reflecting more intensive free-riding under symmetry.