Study on equilibrium strategies for transboundary pollution under competitive conditions

Competitive relationships among players plays an increasing role on transboundary pollution management. In this paper, a transboundary pollution game between two competitive regions as a player is constructed to explore the equilibrium strategies of output and pollution abatement efforts. The dynamic of the pollution stocks for regions are modeled separately in terms of a differential equation. Subsequently, the corresponding equilibrium strategies and value functions are derived in two regimes: Nash non-cooperative and Stackelberg leader–follower games. And the expectation and variances of pollution stocks are calculated over time. Our results are summarized as follows. First, an increase in the proportion of transboundary pollution increases the output of pollution upstream region, decreases the output of pollution downstream region, and ultimately raises the aggregate pollution stock of both regions. Second, regional competitive preference can enhance the local abatement effort and reduce the aggregate pollution stock. Finally, the total social welfare and environmental quality are higher in the Nash non-cooperative game, but pollution downstream region seek to be a leader in the Stackelberg game.