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

Zuliang Lu; Mingsong Li; Longzhou Cao; Junman Li; Zhihui Cao; Zhuran Xiang; Zuliang Lu; Mingsong Li; Longzhou Cao; Junman Li; Zhihui Cao; Zhuran Xiang

doi:10.3934/math.20251079

AIMS Mathematics

2025, Volume 10, Issue 10: 24329-24351. doi: 10.3934/math.20251079

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

1.
Key Laboratory for Nonlinear Science and System Structure, Chongqing Three Gorges University, Chongqing 404000, China
2.
Research Center for Mathematics and Economics, Tianjin University of Finance and Economics, Tianjin 300222, China
3.
School of Computer Science, Chongqing University, Chongqing 400044, China

Received: 23 July 2025 Revised: 17 September 2025 Accepted: 23 September 2025 Published: 24 October 2025
MSC : 49L20, 91B76

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.
- differential game,
- transboundary pollution,
- Runge-Kutta method,
- learning by doing
Citation: Zuliang Lu, Mingsong Li, Longzhou Cao, Junman Li, Zhihui Cao, Zhuran Xiang. A differential game of transboundary pollution in the upper Yangtze river: Ecological compensation and learning-by-doing in the Chongqing-Sichuan region[J]. AIMS Mathematics, 2025, 10(10): 24329-24351. doi: 10.3934/math.20251079

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Abstract

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.

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