A Tripartite Differential Game Approach to Understanding Intelligent Transformation in the Wastewater Treatment Industry

The intelligent transformation of the wastewater treatment industry, as a core component of the modern environmental governance system, is of decisive significance for achieving sustainable development goals. This study focuses on the issue of multi-stakeholder collaborative governance in the intelligent transformation of the wastewater treatment industry, with differential game theory as the core framework. A tripartite game model involving the government, wastewater treatment enterprises, and digital twin platforms is developed to depict the dynamic interrelations and mutual influences of strategy choices, thereby capturing the coordination mechanisms among government regulation, enterprise technology adoption, and platform support in the transformation process. Based on the dynamic optimization properties of differential games, the Hamilton–Jacobi–Bellman (HJB) equation is employed to derive the long-term equilibrium strategies of the three parties, presenting the evolutionary paths under Nash non-cooperative games, Stackelberg games, and tripartite cooperative games. Furthermore, the Sobol global sensitivity analysis is applied to identify key parameters influencing system performance, while the response surface method (RSM) with central composite design (CCD) is used to quantify parameter interaction effects. The findings are as follows: (1) compared with Nash non-cooperative and Stackelberg games, the tripartite cooperative strategy based on the differential game model achieves global optimization of system performance, demonstrating the efficiency-enhancing effect of dynamic collaboration; (2) the most sensitive parameters are β, α, μ₃, and η₃, with β having the highest sensitivity index (STᵢ = 0.459), indicating its dominant role in system performance; (3) significant synergistic enhancement effects are observed among α–β, α–μ₃, and β–μ₃, corresponding, respectively, to the “technology stability–benefit conversion” gain effect, the “technology decay–platform compensation” dynamic balance mechanism, and the “benefit conversion–platform empowerment” performance threshold rule.