基于排放权交易与减排研发补贴的政企减排微分博弈模型

基于碳排放权交易背景，运用微分博弈理论研究了政府与其所辖多个工业企业之间的Stackelberg减排博弈问题，同时还考察了两个地区进行合作减排对政府及企业的策略影响情况。其中，工业企业在生产排放的同时还进行减排技术研发，政府则对企业研发提供补贴。此外，政府对公共资源部分也进行投入，从而实现一定的减排量。通过构造汉密尔顿-雅可比-贝尔曼方程，运用最优控制理论，分析了地区间减排合作与不合作情况下政府对所辖企业的动态补贴策略、自身减排投入策略以及企业的生产及研发策略。通过研究发现，地区间的减排合作使得均衡状态下政府对企业研发补贴量升高，对公共资源减排投入增加，企业自身的减排研发投入也随之增加，从而使得各地区的实际排放量降低。最后，通过算例对相关数据进行分析，验证了模型结论的有效性，从而为政府间的减排合作以及企业制定生产及减排技术研发策略提供了科学依据。

ADifferential Game Model of Government and Enterprise Emission Reduction Basedon Emission Permits Trading and Subsidy for Emission Abatement

Basedon the background of carbon emission trading, this paper studies theStackelberg emission reduction game between the government and many industrialenterprises under its jurisdiction by using the differential game theory.Besides, it also studies the impact of cooperative emission reduction betweentwo regions on the strategies of the government and enterprises.  Enterprises also conduct emission reductionresearch and development while producing emissions, while the governmentprovides research and development subsidies for enterprises. Moreover, byconstructing the Hamilton-Jacobi-Bellman equation and using the optimal controltheory method, it investigates the dynamic subsidy strategies and the emissionabatement strategies of governments and enterprises under the condition ofcooperation and non-cooperation. It can be found that the cooperative game willincrease the research and development subsidies of the government, and theabatement investment of the government and enterprises, thus reducing theactual emissions of each region. The validity of the model conclusion isverified by the analysis of the relevant data in an example. This paperprovides a scientific basis for the cooperation of governments in emissionreduction and the formulation of production and emission reduction research anddevelopment strategies for enterprises.