Where product innovation requires several complementary patents, fragmented property rights can be a factor that limits firms’ willingness to invest in the development and commercialization of new products. This paper studies multiple simultaneous R&D contests for complementary patents and how they interact with patent portfolios that firms may have acquired already. We also consider how this interaction and the intensity of the contests depends on the type of patent trade regimes and the product market equilibria that result from these regimes. We solve for the contest equilibria and show that the multiple patent product involves an important hold-up problem that considerably reduces the overall contest effort