Abstract: With the development of information & knowledge economy and the deepening of economic globalization, Chinese businesses are facing increasingly competitive pressure from the world. Construction of large enterprise groups is becoming a trend. At the same time, with the increase of mergers and acquisitions, and the further expansion of multinational corporations, governance problem brought by the complexity of the enterprise groups is urgent to be solved. Corporate governance should span a single corporate governance boundary, to expand enterprise dimensions, implementation from "Corporate "governance to "group" governance breakthrough.Parent-subsidiary corporate governance is the core issue of corporate governance, parent companies and subsidiaries within the group interconnected and relatively independent relationship has produced a new governance issue, become a problem that influence enterprise groups to exert the overall advantages. In this paper, by using evolutionary game analysis model, and fully considering the dynamic nature of governance and its subsidiary initiative on governance, the mechanism of interaction between supervision strategy of the subsidiary to the parent company and the strategy selection strategy of subsidiary is studied, and the important factors affecting the evolution stability of the system were analyzed.The corporate governance theory is enriched, and a new idea to solve the principal-agent problem between the parent and subsidiary is offered.The results show that the process of the game existed evolutionary stable strategy in 3 cases, but there is no optimal stable strategy. The strategy choices depend on each other's strategy selection probability, the final equilibrium state depends on the parent company learning adjustment speed. Through the design of a reasonable incentive mechanism, such as the introduction of the percentage ratio α that positively related to the income created by the subsidiaries of the group, to increase penalties, take regular or irregular spot checks and other means, the parent-subsidiary company strategy adjustment speed can be affected, the game will turn to the strategy evolution evolution that group profit is the biggest change, or that there is no supervision.And a good relations of mutual trust and benefit between parent company and subsidiary is promoted, the group overall income is increased, the overall superiority of enterprise groups will be strengthen.

Key words: enterprise groups, parent-subsidiary corporation, corporation governance, evolutionary game