Abstract: This paper constructs a three-stage game model of duopoly firms with product differentiation. The government chooses the R &D subsidy rate at the first stage,firm determines its R &D expenditure at the second stage,and firm sets its price under Bertrand competition at the third stage. According to whether the duopoly cooperates in R &D and price stage,this paper gives the government's optimal R &D subsidy rate under five different cases which are competition R &D,cartel R &D,joint lab,technology sharing cartel and research joint venture respectively. It is showed that the subsidy rate under noncooperation R &D case is smaller than that under cartel R &D case while the technology spillover and product differentiation are lower;the subsidy rate under noncooperation R &D case is larger than that under cartel R &D case while the technology spillover and product differentiation are higher. After the government gives the optimal R &D subsidy rate,the strategic Joint Lab is the worst and the strategies of Technology Sharing Cartel and Research Joint Venture are the best in the five strategies through the perspectives of technology progress,output of the firms and the total welfare.

Key words: strategic R &D, government’s subsidy, Bertrand competition, product differentiation, technology spillover