A differential game of transboundary pollution in the upper Yangtze river: Ecological compensation and learning-by-doing in the Chongqing-Sichuan region

This paper investigates a differential game modeling transboundary pollution management in the Upper Yangtze River Basin under noncooperative and cooperative scenarios, incorporating emissions trading, learning-by-doing effects, and abatement investment costs. The maximum principle of optimal control theory was employed to derive equilibrium solutions for both models. Numerical simulations identified optimal emission levels and abatement investments for the Chongqing Municipality and Sichuan Province under each scenario, with the pollution stock trajectories computed using the fourth-order Runge-Kutta method. Numerical validation demonstrated that ecological compensation mechanisms enhance mitigation effectiveness. Furthermore, the study revealed that learning-by-doing efficiency gains and reductions in regional abatement investment costs synergistically enhance both pollution mitigation and economic returns within this framework.