A study on transboundary air pollution based on a game theory model: Cases of SO2 emission reductions in the cities of Changsha, Zhuzhou and Xiangtan in China

China now faces severe air pollution problems while consuming a huge quantity of coal. At present, due to the emission charges and the emissions trading policy failed to effectively prompt enterprises to reduce emissions and improve air quality. Therefore, improving air quality through regional negotiations and cooperation may be feasible and effective. In this study, which was based on game theory, a transboundary air pollution model was established to conduct an empirical study on the cost-effectiveness of cooperative SO2 reduction in three cities of Hunan province in China. Four gain allocation mechanisms, i.e., the nucleolus, Nash-Harsanyi allocation solution, Shapley value and Separable Cost Remaining Benefit (SCRB) principle, were employed to allocate the gains of cooperation, and the fairness and stability of the different allocation mechanisms were also analyzed. The results show that if a gain-sharing mechanism can reasonably allocate the gain from full cooperation, it is then feasible and effective for the three cities to fully cooperate to reduce SO2 emissions. Among the four gain allocation methods investigated in this empirical study, the stabilities of gain allocation for full cooperation using SCRB principle and Nash-Harsanyi allocation method were higher than those using the other two allocation methods. The results provide clear empirical evidence that regional gain allocation may affect the sustainability of cooperation. Therefore, although it was desirable to reduce SO2 emissions through cooperation, the long-term sustainability of cooperation should be taken into account in developing relevant policies.