Because both pollution emissions and production policies often are international in scope, it is necessary to find optimal coordination strategies for international production planning and pollution abating. Differential game models are developed for multiple neighboring countries to reach optimal decisions on their production planning and pollution abating under cap-and-trade regulations. Non-cooperative and cooperative differential games are presented to depict the optimal tradeoffs between production planning and pollution abating. Hamilton-Jacobi-Bellman (HJB) equations are then employed to analyze the asymmetric and symmetric feedback solutions. Numerical simulations are used to illustrate the results. Five different dividends are also discussed. With the proposed strategies, more improvement will be directed toward production supplies and environmental issues than ever before.
Keywords: carbon emission; differential game; optimal coordination strategy; pollution abatement; production plan.