In view of establishing a four-stage R&D rivalry model with R&D spillovers in outputs, it analyzes the effect of R&D spillovers and bargaining power upon the licensing gain within firms on R&D subsidy policy in fixed-fee licensing. The result shows that there is no incentive for the governments to subsidize its firms' R&D when a firm innovates. A government's R&D policy crucially depends on its domestic firm's bargaining power over the licensing gain when both firms innovate. There are three kinds of situations as follows: if the R&D spillover is smaller than one half, the government subsidizes its domestic firm's R&D, while when the firm's bargaining power is greater than the other, the government levies tax on the firm; if the R&D spillover equals one half, a government's R&D policy is also decided by its firm's bargaining power; if the R&D spillover is more than one half, both governments will subsidize R&D investment by their domestic firms.