Abstract: Transboundary pollution occurs when a potentially harmful environmental pollutant is released from one region and then migrates to another. Each region not only suffers from its own emissions damage, but also is affected by emissions from neighboring regions. The traditional mode of pollution control by considering local region has been difficult to effectively solve the current serious transboundary pollution problem, thus, the cooperative mechanism and cost-sharing mechanism have been introduced in this study.
This paper focuses on the transboundary pollution control problem between a developed region and a developing region, the differences between the two regions are reflected in production capacity, abatement costs, and damage cost derived from pollution. Based on the above features, a differential game model between asymmetric regions has been built, where emissions are a by-product of production and accumulate into a harmful stock pollutant. The feedback Nash equilibrium, optimal trajectories of pollution stock and the change of instantaneous revenues are obtained under three scenarios consist of non-cooperative mechanism, pollution control cost-sharing mechanism and cooperative mechanism. Next, the Nash Bargaining solution is further introduced to analyze the optimal allocation strategy of dynamic cooperative payment with time-consistency.
The results show that the pollution control cost-sharing mechanism can achieve Pareto improvement from the point of economy and environment when the environmental damages caused by the pollution are serious, while the cooperative mechanism is optimal in both regional revenues and environment. Secondly, the influences of "myopia" behaviors and environmental self-purification rate on equilibrium strategies in steady state are discussed through numerical analysis. The analysis shows that the "myopia" behavior of the regions leads to the maximization of short-term revenues, thus reducing the investment in pollution control and increases the pollution stock. With the increase of environmental self-purification rate, both pollution stock and revenues for two regions are improved, while the more sensitive for the environmental pollution damage has a more significant increasing in revenue. Finally, the specific numerical changes of dynamic optimal payment distribution are given. The research of this paper is conducive to the government and environmental authority to formulate better policies to solve the problem of transboundary pollution.

Key words: regional pollution, non-cooperative mechanism, pollution control cost-sharing, cooperative mechanism, dynamic payment distribution, differential game