A differential game approach to dynamic optimal control strategies for watershed pollution across regional boundaries under eco-compensation criterion

摘要

In recent years, transboundary pollution reflected by watershed pollution has emerged in an endless stream, manifesting as the overflow phenomenon of one-way or crossing between river basins. Such pollution significantly seriously affects the inherent requirements for achieving regional sustainable and coordinated development in China. By introducing the eco-compensation criterion, a cross-regional boundaries pollution abatement differential game model covering upstream and downstream regions in a continuous time is established. Subsequently, the optimal control theory is adopted by maximizing the net present value of river basin welfare to explore relevant optimal feedback equilibriums on the overall watershed environmental quality under the Stackelberg and cooperative game contracts. Eventually, a case study of Xiang Jiang River Basin (XJRB) in Hunan Province of China serves to verify the practicable effectiveness of the foregoing model combined with numerical simulation and support key insights as below: (i) the watershed environmental degradation cost factor as well as the payoff factor possess significant impact on emission capacities of upstream and downstream; (ii) the optimal trajectory of pollutant stock in the downstream affected by the upstream pollutant stock and pollution transfer coefficient is higher than that in the upstream; (iii) the setting of eco-compensation criterion can effectively stimulate upstream governments to invest more in environmentally friendly technologies; and (iv) the joint decisions of the two game parties improve the total welfare level of both river basin regions. Findings present an efficient approach for the design of environmental policies addressing conflicts over water pollution across regional boundaries.