Government-Industry–University Cooperative Innovation plays an important role for improving national independent innovation ability and promoting scientific and technological innovation and economic development. How to improve the efficiency of collaborative innovation and how to play the guiding role is of great research value on the part of the government to ensure the stability of collaborative innovation system. 
    In the past, most scholars have studied the game evolution strategies of Government-Industry–University Cooperative Innovation, and the strategies choices among during the collaborative innovation process, they exploited the characteristic payoff function of a cooperative game from the factors. The purpose of this paper is to study systemically the measurement of stability of collaborative innovation alliance, and the role of each body in alliance and its development trend. However, as the model of constructing payoff function cannot meet the needs, we modeled the Triple Helix of university-industry-government relationships with game theory, core, Shapley value and nucleolus as indicators of synergy within an innovation system. 
   Triple Helix of Government-Industry–University relationships is a three-person cooperative game with transferable utility. The core, the Shapley value and the nucleolus are suggested as indicators to measure the synergy between innovation actors. The three indicators have different roles in the synergy effect. The core not only expressed the interests of the single factor, but also expressed the whole factors and the constraints around the whole factors exerted on them; The core determines existence and level of synergy within a Triple Helix innovation system, which can be used to measure the extent of the synergy and the stability of innovation coalition. Within the framework of the Triple Helix relationships, the Shapley value is defined as the power of an actor to lead to and create synergy, it can be used to measure the percentage of each contribution factors cause to create synergy which can show the lead factor and strength of the create synergy. The nucleolus indicates the "more acceptable" distribution of the total payoff among players, the basic idea behind the nucleolus is to make the least happy coalition as happy as possible, which can determine the power of coalitions so that to maintain synergy of the systems. The difference between the Shapley values and the nucleolus can measure the contribution of the innovation subject to maintaining the stability of the innovation alliance.
   This paper, on the basis of the triple helix framework, has taken scientific research papers as an indicator to measure the creative product. Knowledge innovation based on scientific research is the foundation and the key of innovation, and knowledge innovation is the foundation of technological progress, so we have collected the scientific research papers from governments, industries and universities since 2006. With the help of the core, Shapley value and nucleolus, this paper has carefully studied through data analysis the changing process of the synergy relationship of government-industry-university in China since 2006 with the following conclusions: 
   (i) From the number of scientific papers published in scientific journals, the ability of collaborative innovation between government, industry and university in China has been increasing year by year, and surpassed the United States in 2012.The scope of the nucleolus of the collaborative innovation between government, industry and university in China has become wider and wider, which illustrates that the ability of collaborative innovation is becoming more and more powerful, and there is a greater space to form collaborative innovation coalition, leading simultaneously to the generation and creation of more synergy effects. The position of the core also indicates the share of each actor in the total revenue of collaborative innovation. Generally speaking, the university has the largest revenue share (80-100%), the revenue share of government is 0-20%, and industry account for less than 5% of the total revenue; 
   (ii) Through the data analysis of the Shapley value, we have found that the main factor leading and producing the synergy effect is university followed by government and the weakest factor is industry. Then over time, we have found that the synergy effect between government, industry and university in China is also changing,the synergy effect of the university is becoming gradually weaken, the synergy effect of the government and industry is becoming gradually strengthen; 
   (iii) The nucleolus may be interpreted as a fair allocation based on the coalitions of which players are a member, through the nucleolus data analysis, we have found that the government plays a role in leading and encouraging the synergy innovation. During the processes of allocating interests, the government has given the biggest share to the universities and industries, and especially to the universities, in order to simulate the motivation and enthusiasm from the universities and industries to participate in collaborative innovation synergy coalitions. This can greatly help to maintain the synergy coalitions more stable, indicating clearly that the government′s giving more benefits to the universities and industries has constituted the main impetus of the increasing synergy innovation and creative achievements in China; 
    (iv) In comparison with the United States, we have found that the synergy effect of collaborative innovation in China is larger than in the United States, and the changing trend of the synergy effect is also more obvious than the United States. However, the contribution from the industry synergy in China is much smaller than in the United States, but the government′s guiding role and contribution in the collaborative innovation coalitions is much greater than in the United States. It indicates definitely that China′s government has been made more efforts in order to generate and maintain the synergy effects than the United States;
    (v) The Chinese government plays an important role in regulating collaborative innovation coalitions during the processes of allocating the interests from the synergy innovation alliances. Traditionally the government has granted more benefits to the universities than to the industries. However, since the industry is an important carrier in translating the knowledge innovation achievements into productivity, therefore, in the near future, it is urgently necessary for the government to stimulate the industry to be involved in the collaborative innovation actively, so as to enable the industry to gain more enthusiasm to participate in tripartite cooperation and innovation. It is necessary for the government to articulate specific policies to promote and guide the industry, and grant it more benefits than ever before.