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

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.