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.

Purpose The authors characterize the conditions under which a country may eventually split and when it splits within an infinite horizon multi-stage differential game. Design/methodology/approach In contrast to the existing literature, the authors do not assume that after splitting, players will adopt Markovian strategies. Instead, the authors assume that while the splitting country plays Markovian, the remaining coalition remains committed to the collective control of pollution and plays open-loop. Findings Within a full linear-quadratic model, the authors characterize the optimal strategies. The authors later compare with the outcomes of the case where the splitting country and the remaining coalition play both Markovian. The authors highlight several interesting results in terms of the implications for long-term pollution levels and the duration of coalitions under heterogenous strategies as compared to Markovian behavior. Originality/value In this paper, the authors have illustrated the richness of the simplications of enlarging the set of strategies in terms of the emergence of coalitions, their duration and the implied welfare levels per player. Varying only three parameters (the technological gap, pollution damage and coalition payoff share distribution across players), the authors have been able to generate, among other findings, quite different rankings of welfare per player depending on whether the remaining coalitions after split play Markovian or stay precommited to the pre-splitting period decisions.

We characterize the shape of spatial externalities in a continuous time and space differential game with transboundary pollution. We posit a realistic spatiotemporal law of motion for pollution (diffusion and advection), and tackle spatiotemporal non-cooperative (and cooperative) differential games. Precisely, we consider a circle partitioned into several states where a local authority decides autonomously about its investment, production and depollution strategies over time knowing that investment/production generates pollution, and pollution is transboundary. The time horizon is infinite. We allow for a rich set of geographic heterogeneities across states. We solve analytically the induced non-cooperative differential game and characterize its long-term spatial distributions. In particular, we prove that there exist a Perfect Markov Equilibrium, unique among the class of the affine feedbacks. We further provide with a full exploration of the free riding problem and the associated border effect.