Abstract: Based on the classic duopoly games and branch theory of dynamic system and chaos economics principle, this paper creates a dynamic model of R&D competition with government R&D subsidy, analyzing the effects of R&D subsidy on the R&D competition’s Nash equilibrium and the whole market operation, while a numerical simulation is carried out. The research shows that: (1) Appropriate subsidy rates are largely limited by market demand function, adjustment speed of R&D investment and product costs. Keeping R&D subsidy rates within certain range helps system maintain equilibrium states. In other words, bifurcation or chaos could happen if R&D subsidy coefficient falls out of range. (2) In the early stage of subsidy policy, the market could be in a short unstable state, in which the fluctuation range of R&D investment is larger than that of profit margin, and both of them have a positive relationship with government R&D subsidy rates. (3) Public R&D subsidies encourage corporations to increase R&D investment and enable corporations with faster adjustment speed to obtain higher return in dynamic duopoly games. At last, suggestions of subsidy strategies at policy level are given to provide reference for relevant R&D subsidy policy formulation.

Key words: R&D competition, bounded rationality, chaos