Abstract: From the perspective of multiple pollutants (non-cumulative and cumulative pollutants) causing different damage to the environment and ecological compensation mechanisms, the optimal control theory is used to construct a game model of optimal control of transboundary pollution in two adjacent areas composed of the acceptance area and the compensation area. The strategies of environmental pollution control under Stackelberg non-cooperative game and cooperative game are analyzed, including pollutant emission, investment in environmental pollution control and ecological compensation coefficient. At the same time, the dynamic changes of pollutant stock and investment stock of environmental pollution control are discussed, and the optimal solutions in these two cases are compared and analyzed. The theoretical and simulation analysis results show that the optimal ecological compensation coefficient of the compensation area under the Stackelberg game only depends on the income of environmental management in these two regions, but has nothing to do with other factors. However, under the cooperative game, each region will consider the losses caused by its non-cumulative pollutant emission to its neighbors, and the region will increase investment in environmental pollution control. The cooperative surplus is affected by the damage of cumulative pollutants stock and the damage of non-cumulative pollutants to adjacent areas, but it is not related to the damage of noncumulative pollutants to its own area. Whether it is Stackelberg non-cooperative game or cooperative game, the pollutant stock and pollution control investment stock are affected by their initial stock and other factors, showing a diversified dynamic path.

Key words: ecological compensation, cooperative governance, transboundary pollution, non-accumulative pollutants, accumulative pollutants