The irreversible pollution game

Abstract

We investigate the extent to which the irreversibility of pollution shapes the free-riding problems inherent in pollution (differential) games. To this end, we use two-country differential pollution games. Irreversibility is of a hard type: While strictly positive and concave below a certain threshold level of pollution, pollution decay drops to zero above this threshold. Assuming that the pollution damage function and preferences are quadratic, we first examine both the cooperative and non-cooperative versions of the game. We innovate in analytically demonstrating the existence of Markov perfect equilibria (MPE) and characterizing these. Second, we demonstrate that when players face the same pollution costs (symmetry), irreversible pollution regimes are more frequently reached than under cooperation, and we evaluate the irreversibility penalty stemming from the absence of cooperation. Incidentally, we prove that open-loop Nash equilibria lead to reach more frequently the irreversible regime than the MPE under our setting. Third, we study the implications of asymmetry in the pollution cost. We find that for equal total pollution costs, asymmetric equilibria produce a lower emission rate than the symmetric under some mild conditions, thereby driving the system to irreversibility less frequently than the latter. Finally, we prove that provided the irreversible regime is reached in both the symmetric and asymmetric cases, long-term pollution is greater in the symmetric case, reflecting more intensive free-riding under symmetry.