R&D, patents and innovation: a differential game approach

A patent race is a technological competition among firms and the firm making a first-hand innovation takes advantages of patenting. Firms strategically invest in R&D and produce knowledge in order to innovate. Instead of growing model of R&D, I use a differential game approach to investigate firms interaction of R&D behavior in a patent race. In general, knowledge is an intangible good that gives a special feature of a patent race. Whether knowledge is substitutable to the existing knowledge pool affects firm’s incentives to invest in R&D. After innovating successfully, the innovator patents on its techniques so that their opponents cannot infringe. However, a patent system indirectly ensures the monopoly power of the innovator in a product market, which reduces the social welfare. I evaluate the endogenous benefit of a patent holder and suggest an optimal patent policy in order to balance out the loss of the social welfare and innovation incentives. Besides, production usually contains several techniques with different patents and this collection forms a patent portfolio. Even though the patent war is nothing new, there is still innovation developed by users volunteering without any patenting in the market. A model of a patent portfolio race explains why some innovation such as an open-source software without patenting can also be as successful as a private software product.