Payments for environmental services strategy for transboundary air pollution: A stochastic differential game perspective

Air pollution has become a global threat to societal development. The main challenges of transboundary air pollution control include two perspectives: uneven socioeconomic development of regions and the diffusion of air pollution. This paper proposes an PES strategy to alleviate transboundary air pollution by coordinating regional economic interests and environmental preferences within the joint prevention and control of air pollution region. To make the model de-sign more realistic, we introduce the stochastic differential game model to characterize the diffusion and uncertainty of air pollution. The optimal feedback Nash equilibrium is derived in three PES scenarios (no PES, dynamic PES, and fixed-fee PES) by using the Hamilton-Jacobi-Bellman equation. Numerical simulations and sensitivity analysis are im-plemented to compare the optimal strategies under the three PES scenarios. The dynamic PES strategy is shown to out-perform the no PES strategy and the fixed-fee PES strategy by encouraging the backward region to cut more emissions. Besides, the confidence interval theory is used to estimate the variation range of air pollution stocks, which provides a powerful diagnostic tool for policy-makers.