Optimal control for transboundary pollution under ecological compensation: A stochastic differential game approach

Abstract To account for previously ignored, yet widely observed uncertainty in nature's capability to replenish the natural environment in ways that should inform ideal design of ecological compensation (EC) regimes, this study constructs a stochastic differential game (SDG) model to analyze transboundary pollution control options between a compensating and compensated region. Equilibrium strategies in the stochastic, two player game inform optimal control theory and reveal a welfare distribution mechanism to form the basis of an improved cooperative game contract. A case-based numerical example serves to verify the theoretical results and supports three key insights. First, accounting for various random disturbance factors, the probabilistic pollutant stock in Stackelberg non-cooperative game exceeds that of a cooperative game situation. Second, the EC mechanism provides long-term, effective incentives only when the marginal losses of environmental damage in the compensating region are more than twice that of the compensated region. Achieving a Pareto optimal equilibrium relies upon the attainment of a dynamic allocation ratio derived from the analysis of a robust welfare allocation mechanism. Third, cross-region cooperation reliably outperforms Stackelberg non-cooperation due to either overwhelming incumbent economic interests or high abatement costs. This study illuminates the importance of balancing both parties' interests within an EC agreement while reducing uncertainty around unobserved environmental factors during ex-ante negotiations.