In the context of green development, cooperation between government and enterprises in emission reduction is an effective way to improve the efficiency of enterprise emission reduction. In carbon trading policies, this paper assumes that the consumer demand influenced by product green level and enterprise goodwill, considering the continuous production in a multiple cycle under the condition of dynamic change characteristics, constructs the government and enterprise cooperation to reduce emissions of three kinds of differential game model, to explore the effective way of government and enterprise cooperation. The results show that cost-sharing contracts can achieve Pareto improvement of revenue for the government, enterprise under a certain condition; the revenue of the government, enterprises, and systems are optimal under collaborative cooperation. Finally, we prove the validity of the conclusion through an example analysis, and the sensitivity of related parameters is analyzed.