Optimal decision for multi-pollutants problem under ecological compensation mechanism and learning by doing

Multi-pollutants transboundary pollution is a complicated problem, for such problems, the research involves the attributes of pollutants, the degree of separability, whether the abatement cost is separable, etc. To address these challenges, this paper discusses the problem of multi-pollutant transboundary pollution based on differential game theory under the learning by doing and ecological compensation mechanism. Using the dynamic optimal control theory, we obtain the optimal equilibrium strategy under the noncooperation and cooperation model between the two regions and analyze the influence of multi-pollutants characteristics and other parameters on the optimal equilibrium strategy. In our model, the pollutants can be either technological substitutes or complements which are not necessarily separable, and the abatement costs of two pollutants are not separable. Through numerical simulation, the results show that (i) The two pollutants are substitutes or supplements which have no impact on the emission levels of these two pollutants, and as the degree of the inseparability of the two pollutants increases, the emission level decreases gradually; (ii) The abatement investment level of the two pollutants are substitutes is higher than the two pollutants are complements, and the abatement investment level increases with the degree of inseparable under the cooperation and noncooperation models; (iii) The pollution stocks of two pollutants are substitutes is higher than the two pollutants are complements.