In order to achieve carbon peak and neutrality goals, this study takes product innovation as the breakthrough point, draws lessons from the replication dynamic thought of the biological evolution process, and uses game evolutionary algorithm to analyze the gradual stability of enterprises, governments and users. Although the environment does not actively participate in the game, its benefits directly affect the strategic choices of the other three parties. Therefore, the environmental benefit is regarded as one of the important variables to establish a game model for solving and simulation, and analyze the key variables affecting the game. This paper discusses the game situation of green product innovation in the evolutionary system for promoting “four-party satisfaction”. The concepts of proactive preventive cost and passive loss cost are redefined and put forward. Research shows that: (1) Proactive preventive cost plays a positive role in promoting green product innovation with “four-party satisfaction”. (2) Increasing subsidies for purchasing green products, reducing the price of green products, increasing purchase tax on non-green products, and increasing government investment in environmental protection publicity and green upgrade of infrastructure will all increase users’ willingness to buy green products. (3) The government formulates reasonable reward and punishment measures to provide necessary financial support for enterprises, so that the final income of enterprises from green product innovation is greater than that from traditional product innovation. It will encourage enterprises to carry out green product innovation.