We investigate how the relationship between capital accumulation and pollution is affected by the source of pollution: production or consumption. We are interested in polluting waste that cannot be naturally absorbed, but for which recycling efforts aim to avoid massive pollution accumulation with harmful consequences in the long run. Based on both environmental and social welfare perspectives, we determine how the interaction between growth and polluting waste accumulation is affected by the source of pollution, i.e., either consumption or production, and by the fact that recycling may or may not act as an income generator, i.e., either capital-improving or capital-neutral recycling efforts. Several new results are extracted regarding optimal recycling policy and the shape of the relationship between production and pollution. Beside the latter concern, we show both analytically and numerically that the optimal control of waste through recycling allows to reaching larger (resp., lower) consumption and capital stock levels under consumption-based waste compared to production-based waste while the latter permits to reach lower stocks of waste through lower recycling efforts.

We propose an alternative dynamic theory of coalition breakdown. Motivated by recent coalition-splitting events of unilateral country withdrawals, we assume that: (i) the payoff-sharing rule within coalitions is not necessarily set according to any optimality and/or stability criterion and (ii) players initially behave as if the coalition will last forever. If the sharing rule is non-negotiable or if renegotiation is very costly, compliance with these rules may become unbearable for a given member because the rule, being too rigid, would make exit preferable as time passes. We examine this endogenous exit problem in the case of time-invariant sharing rules. Assuming a Nash non-cooperative game after a (potential) split where players play Markovian strategies, we characterize the solutions of the endogenous exit problem in a linear-quadratic frame with endogenous splitting time. We find that splitting countries are precisely those that used to benefit the most from the coalition. Suitable sharing rules should be used to prevent coalition splitting. When initial pollution is high, all shares should be low enough and none of the players should receive a payoff share larger than 1/2. If initial pollution is low, we provide an explicit interval for sharing-rule values to prevent the collapse of the coalition. Finally, we demonstrate that the latter properties are qualitatively consistent with the optimal behaviors and equilibrium outcomes resulting from players anticipating the end of the coalition and acting accordingly.

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.