Cumulative innovation, open source, and distance to frontier

We develop a multistage game in which firms do cumulative research and development (R&D) to complete a lengthy process, and we study whether firms patent intermediate results or release them in Open Source. A patent holder obtains a larger reward in the market, but since in equilibrium it forecloses R&D, it remains alone to complete the process and so pays a larger cost than an Open Source firm. We have Open Source equilibria when R&D is highly complementary, R&D costs are large, and firms are sufficiently different and far from the frontier. We identify two market failures, in the forms of free riding and coordination failure, and we discuss public intervention.