Abstract: The carbon market is an important means to achieve the dual carbon goals. In the early stages of carbon market operation, China adopted a free allocation method for quota allocation of industries included in the carbon market. In the future, a paid allocation method will be adopted in a timely manner. To explore the factors that affect enterprises in carbon market trading and government regulatory strategies under the paid allocation system, an evolutionary game model between the government and enterprises was constructed. The stable strategy of system evolution in different scenarios was determined, and relevant data was selected for simulation analysis. The analysis results showed that under the paid allocation system of carbon quotas, there are different evolutionary game results between the government and enterprises, and the strategic choices of various entities affect each other. The strategic choices of the central government will be influenced by local governments, but as a policy, they will be influenced by local governments. The promoter always chooses a strict regulatory strategy; The transaction cost of enterprises has a negative impact on trading enterprises. In the early stage of carbon market construction, the government should not only lead the search for trading partners for enterprises, but also provide corresponding trading rewards to both parties; As the number of enterprises participating in carbon trading gradually increases, the central government's strategic choices will also change due to regulatory costs. Starting from the main body of the four party game, this article provides systematic theoretical guidance for the carbon market trading system and operating mode under the paid distribution system.