Regional coalition of basin water pollution control based on differential game

Basin water pollution control has become a real and serious challenge in building an environmentally friendly and resource conserving society. Since water is quasi-public property, regional coalitions become inevitable and possible for the upstream and downstream interests of the basin. This paper takes three regions of the basin as the research object. Compared with previous studies which only consider specific forms, this paper focuses on the generalization of pairwise coalition types. We construct self-sufficient type, side-coalition type, pairwise coalition type, and big coalition type regional coalition models via a differential game method in continuous time. Furthermore, we solved the issue for how to share interests. Subsequently, the Bellman dynamic programming method is adopted to solve these models, and the instantaneous profit of each model is compared at each time point and changes in pollution stocks. Finally, through numerical simulation analysis, results show that the best method of pollution control is the first case of side-coalition (region 1 and region 2 form a coalition, region 3 independence), which can effectively protect the ecological environment of the basin, promoting the sustainable economic development of the whole basin.