As one of the most efficient means of emission reduction policies, carbon quota trading has a far-reaching impact on the carbon emission reduction of enterprises. Firstly, a two-party evolutionary game model of enterprise and government and a three-party evolutionary game model of enterprise–enterprise–government are constructed based on the multi-agent driving mechanism, evolutionary game theory, scenario simulation, and other methods. Then, we conduct a series of policy simulations for carbon emission under different scenario models and various enforcement strengths. Lastly, the behavioral strategies and system evolution trajectories in enterprises and government carbon trading are comprehensively investigated. The results show that in the two-party and three-party evolutionary game models, the carbon trading behavior is affected by the joint action of the enterprise and the government. The difference in initial willingness mainly affects the speed of the subject’s convergence to the steady state. Based on this, policy suggestions are proposed, such as reducing the cost of carbon emission of enterprises, enhancing the vitality of carbon emission reduction of enterprises, and stimulating the power of government regulation and responsibility performance, which can provide suggestions for the development of the carbon market.