针对我国企业,特别是中小企业普遍存在的自主创新不足问题,本文运用博弈论方法,构建在技术外溢条件下的企业自主创新投入模型并进行分析.研究表明:企业从自身利益出发,更倾向于依赖其他企业的自主创新投入.特别是技术落后的中小企业,当企业规模差距扩大时,更增加对技术领先大企业自主创新的依赖性.而企业数量、规模大小、技术外溢系数、自主创新相对重要程度等是影响企业自主创新投入的重要因素.%Abstract: Increasing labor and raw materials costs are leveling out the traditional cost advantage of Chinese enterprises. The 2008 financial crisis raised the major issue that small-and medium- sized enterprises (SMEs) in China lack of the ability to develop their own technology. The objectives of this paper are to explore reasons causing the innovation deficiency of Chinese SMEs and potentials solutions to this persistent problem.Existing literature explores SMEs' innovation deficiency problems mainly from the perspectives of capital inputs, market systems,etc. Their findings are usually not based on a rigorous analysis of economics models and needs further examination. To overcome this challenge, this paper proposes a rigorous theoretical model by laying a theoretical foundation and providing a new research direction to address the innovation deficiency problems of Chinese SMEs. We create a game model to illustrate SMEs' innovation inputs under the technology spillover condition. Based on the game theory, our model assumes that SMEs can benefit from the increase of innovation ability under the technology spillover condition. This model can also help optimize the innovation inputs of SMEs using a production function that is a form of the Cobb - Douglas production function.First, we explore a game of modeling a single enterprise's innovation inputs. The model analysis indicates that under the technology spillover condition an enterprise should consider increasing independent innovation inputs in order to maximize its profits.We further analyze the Pareto Optimality condition from the perspective of social optimization. Our analysis shows that the more a SME can optimize innovation inputs the less other SMEs can do so under the Pareto Optimality condition. In other words, a company will reduce its independent innovation inputs if other SMEs increase their inputs. This dependence will eventually lead to the loss of the entire social welfare.Second, we explore two types of companies using the proposed game: ( 1 ) large enterprises with advanced technology, and ( 2 ) SMEs with less advanced technology. The former will put more efforts in nurturing the ability to innovate independently than the latter,according to the Nash equilibrium. As the gap of efforts in innovation independence continuously widens between large enterprises and SMEs, SMEs will decrease their innovation independence efforts to zero. Eventually, SMEs will completely depend on the innovation capability of large enterprises. A vicious cycle of innovation dependence from large enterprises to SMEs will be created passively. This finding corroborates with the real situation that the majority of SMEs in China are depending too much on the supply of advanced technology by large enterprises to become innovation independent.Third, we conduct a comparative static analysis to assess the effect of enterprise sizes, quantity, technology spillover coefficient,independent innovation and non-independent innovation on the proposed model. If differences in company size and other conditions are fixed, the independent innovation inputs of large enterprises will change in the opposite direction of the quantity change, and in the same direction of scale changes of SMEs. When the size difference is enlarged to a certain degree, large enterprises' independent innovation inputs will change in the opposite direction of its quantity change and in the same direction of scale change of SMEs Size difference is unrelated with the number of SMEs. These findings indicate that enlarging an enterprises' scale will improve that enterprises' innovation independence. Many policies, such as promoting intellectual property and reducing the risks of innovation independence, can decrease the degree of innovation dependence of SMEs on large enterprises. Numerical examples are provided in the end of this paper to analyze the model and validate the analysis results.In summary, although all enterprises would like to achieve innovation independence they have the tendency to depend on another enterprise for innovation. SMEs are usually unwilling to invest in innovative technologies because they cannot afford the investment risks. On the other hand, large enterprises intend to invest in advanced technology in order to maintain and enlarge their competitive advantages over SMEs. If the scale differences between large enterprises and SMEs are too large, SMEs will depend on large enterprises for the development of innovation completely. It is important for SMEs to increase their scale and construct a system to protect their intellectual properties.
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