Abstract: This paper considers a duopolistic model where the two firms both conduct R&D activities with spillovers.Each firm decides its R&D investment before they compete in the product market.According to whether cooperation exists in R&D stage and output stage,the paper studies the spillover levels that maximize the profits of the firms under three cases.The effects of change of spillovers on R&D expenditures,outputs,profits,consumer surplus and social welfare are analyzed under every case.

Key words: R&D, spillovers, cooperation, Cournot equilibrium, Nash equilibrium