The core enterprise oriented entrepreneurship ecosystem plays an important role in promoting the sustainable development of innovation and entrepreneurship and realizing the multi-agent win-win symbiosis. Based on the structure of the core enterprise oriented entrepreneurship ecosystem, this paper constructs an evolutionary game model with the participation of core enterprises, start-up enterprises and the government, analyzes the equilibrium point and corresponding stability conditions for the evolutionary game model, and carries out a simulation analysis on different stability conditions from the aspects of the initial willingness of the participants, the intensity of the subsidy and punishment, the cost and benefit of the strategy selection. The results show that: (1) In order to achieve different equilibrium states, different stability conditions should be satisfied, and there may be multiple stable points under each stability condition. (2) The initial intention will positively affect the subject's positive strategy selection, and negatively affect the subject's negative strategy selection. (3) The strategy selections of core enterprises, start-up enterprises and the government will be affected by many factors, and different factors have different influences on the directions and degrees of the main strategy selections. Based on these conclusions, we can build a unified information platform, set up a moderately high, flexible reward and punishment mechanism, and build a multi-party collaborative governance system. In addition, we can also use the stability conditions to judge the development status of the ecosystem to promote the formation of the ideal core enterprise oriented entrepreneurship ecosystem.INDEX TERMS Core enterprises, entrepreneurship ecosystem, evolutionary game, influence factors.