Cooperative Strategies in Transboundary Water Pollution Control: A Differential Game Approach

Abstract

This paper, based on differential game theory, examines governance models and cooperative strategies for managing cross-border water pollution in regions with uneven economic development. To address cross-regional water pollution, three differential game models are constructed under different scenarios: the Nash noncooperative mechanism, the pollution control cost compensation mechanism, and the collaborative cooperation mechanism. This study analyzes the dynamic changes in pollution emissions, governance investments, and economic returns within each model. The results indicate that the collaborative cooperation mechanism is the most effective, as it significantly reduces pollution emissions, maximizes overall regional benefits, and achieves Pareto optimality. In comparison, the pollution control cost compensation mechanism is suboptimal under certain conditions, while the Nash noncooperative mechanism is the least efficient, resulting in the highest pollution emissions. Furthermore, the research explores the influence of cooperation costs on the selection of governance models. It finds that high cooperation costs reduce local governments’ willingness to engage in collaborative cooperation. However, an appropriate compensation mechanism can effectively encourage less-developed regions to participate. Numerical analysis confirms the dynamic evolution of pollution stocks and economic returns under different models, and provides corresponding policy recommendations. This paper offers theoretical insights and practical guidance for cross-regional water pollution management, highlighting the importance of regional cooperation and cost-sharing in environmental governance.