Abstract: “Building the national innovation system and strengthening the scientific and technological capabilities” was put forward on the 19th National Congress of the Communist Party of China. In recent years, government subsidies have played an critical role in improving the industrial innovation capabilities especially on the Chinese strategic emerging industries which are mostly high-tech industries. However, there are a lot of arguments against government subsidies which will improve the industrial innovation capabilities and might push the private innovation funds out.
Developing countries and emerging enterprises might get their competitive advantages and reduce catching-up processes by learning foreign technologies through continuous adaptive innovation. China, a developing country, is in urgent need of strengthening researches which are aimed at improving high-tech industry continuous adaptive innovation at present by government subsidies.
Technology S curve is a traditional method of analyzing these problems and has always been used by scholars. Even if theoretical analysis has been conducted, few empirical analysis was carried on. This paper uses a regression of technology S curve through Gaussian function curve fitting. Random variables describe the initial state of participants, which matches with the reality.
In this study, our mathematical framework mainly contains three sections. First,this study collected and disposed two decades data from 1995 to 2015 which is based on a official document——Classification of High-tech Industries (Manufacturing Industry) (2017). After unifying the income of new products and specifying initial time points, we used the software MATLAB R2012a to conduct the fitting analysis of Gaussian function and its deformation. R2 (coefficient of determination), SSE (Sum squared error performance function) and RMSE (Root-mean-square error) are three factors which provide measures of how well observed outcomes are replicated by the model. Second, this mathematical model considers a game with two limited rational enterprises (players) who product homogeneous products and choose different technological innovation stages. This paper only takes pure strategies and simultaneous strategies into consideration neglecting mixed strategies and sequential strategies. There are a series of hypothetical premises. Each enterprise has to make a selection either by choosing incremental technology innovation or choosing radical technology innovation. ci denote the marginal cost of product respectively, fixed costs of two enterprises are zero. i denote enterprise i. Enterprise i has a marginal cost ci. tij denotes the initial stage of enterprise respectively. Enterprise chooses radical technology innovation stage, which is denoted j=1. Enterprise chooses incremental technology innovation stage, which is denoted j=2.wi denote the research and development skills of unit product respectively.P(Q)=a－eQ denote the inverse demand function, while Q=q1+q2.a denote the capacity of market. e denote the scope of inverse demand function. qi denote the output of new product. Both of the enterprises make their outputs decisions independently without knowing competitors information. Ii denote the initial investments.y=Ae－(〖SX(t－BΦSX))2denote the stage of product. Adenote the maximum yield.B denote the maximum time point. Φ denote the deviation of figure. ri denote the coefficient of government subsidies. The enterprise who chooses radical technology innovation receives a higher subsidy coefficient from initial investments and innovation products. Nevertheless, the enterprise who chooses incremental technology innovation only receives subsidies from initial investments. Third, let us define a two dimensional payoff matrix based on individual revenue function under the condition of government innovation subsidy policy. Using evolutionary method and thought establishes two replicator dynamics equations and analyzes the equilibrium points.We can investigate the stability of an equilibrium point for a system of nonlinear equations and analyze the local stability.
After simulating Gaussian function and setting up the mathematical model, we have three main findings:(1) The initial technological innovation conditions of enterprises and competitors within the high-tech industry directly affect the overall continuous adaptive innovation behavior of the high-tech industry. If the proportion of enterprise choosing radical technology innovation is high, other incremental technology innovation enterprises tend to choose radical technology innovation to enlarge their competitive advantages and improve their performances. Therefore, when making a new policy, government should not only support the enterprises whose initial resources are sufficient to improve continuous adaptive innovation, but also consider to cultivate the technological innovation capacities of relevant enterprises. (2) Under the government subsidy policies, the high-tech industry which has larger market needs less time to reach the stable state, tending to choose radical technology innovation to enlarge their competitive advantages and improve their performances. The variation of slope of inverse demand curve changes the evolutionary direction, path and the time to reach the stable state. The levels of high-tech innovation are effected by different market demand elasticity. These results have corresponding conditions of domestic development of high-tech industries, such as China Mobile Communications Group. Compared with other industries,this industry has a significant ability of continuous innovation. It is attribute to the strong government support and the fact that China has the largest mobile communication market. Therefore, when making a new policy, government needs to take a lot of factors into consideration, such as market, demand elasticity to optimize innovation behaviors of industry. (3) Under the government subsidy policies, high-tech industries which have lower marginal costs need less time to reach the stable state, tending to choose radical technology innovation to enlarge their competitive advantages and improve their performances. High level subsidies reduce the time to reach the stable state.Therefore, when making a new policy, government needs to investigate the endowments of industries in detail. Increasing the intensity of subsidies and giving marginal cost advantage enterprises some priorities are effective methods that policy makers can use to rise the capacity of continuous adaptive innovation.
An evolutionary game with two groups of players has been proposed in this study for describing the stages of players’ technology innovation under the government subsidies. Finally, this study has the following limitations. (1) This paper doesn’t consider other participants such as research institution, but only considers pure behavior strategies and two players under the limitations of this evolutionary model. For further research, an evolutionary model which contains multiple participants could be set up. (2) This paper neglects the chain effects that individual decision might be affected by other participants. For further research, an evolutionary model which contains chain effect could be set up.

Key words: continuous adaptive innovation, government subsidies, evolutionary game, high-tech industry