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Emission trading scheme (ETS) is considered as a tool to reduce emissions at a low cost, which can effectively promote the carbon peak and carbon neutrality. As the main participants in the carbon emission trading (CET) market, the behavior and strategies for governments and different types of enterprises affect the final emission reduction performance. Taking the national carbon market as an example, this paper constructs a tripartite evolutionary game model including governments and power generation enterprises with different emission reduction capacity to analyze the possible game situations in the development process of the CET market. The results show that with the development of the CET market, the governments and power generation enterprises will have different game results. In order to achieve the optimal stable equilibrium and maximize carbon emission reduction, governments should improve regulatory efficiency and formulate appropriate incentive strategies for excess emission reduction and punishment strategies for insufficient emission reduction. In addition, the initial willingness will not affect the final strategy choice of the three parties. Reasonable free carbon quota ratio, lower technology emission reduction cost and higher carbon price can stimulate the enthusiasm of governments and enterprises to reduce emissions. The above results provide a reference for coordinating the relationships between governments and power generation enterprises with different emission reduction capacity in the construction of the CET market in the future. [ABSTRACT FROM AUTHOR]