Innovation subsidy under duopoly

Innovation plays extremely important roles in the society, and underinvestment in innovation popularly exists. This article aims to capture innovative subsidy with game theory model. First, unilateral subsidy stimulates both innovation and outputs of subsidized firms, while it deters those of opponents. Second, under innovation subsidy, relationship between subsidized firm's innovation and product substitutability satisfies a U shape. For opponents, it is also a U-shaped relationship. Third, under unilateral subsidy, subsidizing high-efficiency firms yields more innovation than subsidizing low-efficiency firms. Finally, bilateral subsidy stimulates more innovation than unilateral subsidy. This study supports theory to subsidize innovation efficiently.