A Decision Support System Based on Stochastic Differential Game Model in Pollution Control Chain

The low enthusiasm for upstream and downstream pollution control is the main factor leading to poor water quality. Optimizing water pollution control strategies for multiple stakeholders/entities in river basins is challenging. Considering the dynamic change of water quality, we study the optimal decision of pollution control chain composed of upstream and downstream. We construct a stochastic differential game model of upstream and downstream efforts to determine the optimal pollution control strategy. The differential evolution algorithm is used to determine the quantity of virtual currencies issued, and the optimal control theory is employed to make decisions on pollution control efforts. We discuss the optimal-feedback equilibrium of watershed environmental quality for three scenarios: 1) no transaction; 2) downstream purchase currency; and 3) upstream purchase currency. As a result, introducing the "water quality-currency" market: 1) improves water quality, increases each entity's pollution control efforts, and forms a mechanism between pollution control efforts and water quality; 2) increases entities' welfare amid increasing volatility, enhancing their resistance to external interferences; and 3) enables the improvement of water and the increase of the entities' profits to be realized at the same time in the downstream purchase scenario.