Transboundary emission under Stochastic Differential Game

In this study we provide a more robust transboundary industrial pollution reduction strategy for global emission collaborations. We consider the dynamics of each country’s quantity of pollution as a Brownian motion with Jumps to capture the systematic jumps caused by surprise effects arising from policy uncertainties within the economy. When the output of each country’s domestic consumption good production is proportional to the level of pollution emissions, we apply optimal control theory to find the Nash noncooperative, cooperative and Stackelberg optimal emission paths. To formulate this problem we allow each country’s discounted stream of net revenues to be maximized via a Stochastic Differential Game (SDG). We then articulate the Nash noncooperative equilibria, cooperative equilibria and Stackelberg equilibria via a feedback control strategy. We show that the outcome of the game depends on the parameters of the game and the type of equilibrium one considers. Furthermore, in this continuous-time differential game paradigm model we show that the feedback Stackelberg equilibrium will not coincide with the feedback Nash noncooperative equilibrium. In this setting, if the first mover advantage of the leader (Player I) disappears then both equilibria coincide.