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Volume 16
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10.3390/su16030944
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Article

The Design of Ecological Compensation for Air Pollution Based on Differential Game

by
Enquan Luo
1,
Zuopeng Hu
2,
Shuwen Xiang
1,
Yanlong Yang
2,* and
Zhijun Hu
2
1
College of Management, Guizhou University, Guiyang 550025, China
2
College of Mathematics and Statistics, Guizhou University, Guiyang 550025, China
*
Author to whom correspondence should be addressed.
Sustainability 2024, 16(3), 944; https://doi.org/10.3390/su16030944
Submission received: 18 December 2023 / Revised: 12 January 2024 / Accepted: 16 January 2024 / Published: 23 January 2024
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Abstract

Establishing a scientific ecological compensation mechanism for air pollution is crucial for air protection. This study models the ecological compensation mechanism of the Stackelberg differential game between the local regulator and an enterprise with a competitor by introducing the air quality index and the social welfare benefits of the local regulator. Using the Pontryagin maximum principle, this study obtains dynamic strategies for the local regulator and the enterprise while maximizing the benefits. The evolution of the shadow price is analyzed with the inverse differential equation method. Then, the effects of the shadow price on the optimal dynamic strategies are analyzed using numerical simulation, together with the effects of the introduction of social welfare benefits on the efforts of the local regulator to protect the air environment. The conclusions show that introducing social welfare benefits as an ecological compensation criterion for air pollution promotes air protection by the local regulator.
Keywords: differential game; ecological compensation; air pollution index; Pontryagin maximum principle differential game; ecological compensation; air pollution index; Pontryagin maximum principle

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MDPI and ACS Style

Luo, E.; Hu, Z.; Xiang, S.; Yang, Y.; Hu, Z. The Design of Ecological Compensation for Air Pollution Based on Differential Game. Sustainability 2024, 16, 944. https://doi.org/10.3390/su16030944

AMA Style

Luo E, Hu Z, Xiang S, Yang Y, Hu Z. The Design of Ecological Compensation for Air Pollution Based on Differential Game. Sustainability. 2024; 16(3):944. https://doi.org/10.3390/su16030944

Chicago/Turabian Style

Luo, Enquan, Zuopeng Hu, Shuwen Xiang, Yanlong Yang, and Zhijun Hu. 2024. "The Design of Ecological Compensation for Air Pollution Based on Differential Game" Sustainability 16, no. 3: 944. https://doi.org/10.3390/su16030944

APA Style

Luo, E., Hu, Z., Xiang, S., Yang, Y., & Hu, Z. (2024). The Design of Ecological Compensation for Air Pollution Based on Differential Game. Sustainability, 16(3), 944. https://doi.org/10.3390/su16030944

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