Abstract: Aiming at the analysis of the effect of government research and development (R&D) subsidy policies on the firm’s performance in a duopoly market, a three stage game model is established. The first stage is for the government R&D subsidy situation, including: 1) the government gives the subsidy for the R&D investment of a firm; (2) the government gives the subsidy to encourage a firm for R&D in product innovation. They are called the first and second subsidy policies. In this stage, the government determines the R&D subsidy rate to maximize the total social welfare. The second stage models the R&D cooperation between enterprises and the enterprises determine the R&D level to maximize the total profit. The third stage is for product competition and the enterprises determine the output level to maximize their profit. Based on the model, by means of backward induction, the CournotNash equilibrium solutions under R&D cartel strategy are acquired. It shows that, when the cartel R&D strategy is applied, the government subsidy rate resulting from the second policy is much greater than that resulting from the first policy. Thus, the second R&D subsidy policy is superior to the first one, for it makes the firms to invest less but create more output, profit, and social total welfare.

Key words: Cournot competition, research and development (R&D); government R&D subsidy