A dynamic model of open source vs proprietary R&D

We propose a dynamic model in which firms compete to produce sequential and cumulative innovations, and in which the more firms do research in one sector the more likely it is that one of them innovates. Firms choose research effort and whether to patent innovations or to use an Open Source license like the General Public License. We show that (i) patents generate a larger stationary reward but foreclose research within a sector, and that (ii) Open Source generates a smaller stationary reward but allows everyone to use the technology, and therefore, by attracting firms to the sector, it induces a faster pace of innovation. We characterize all the equilibria of the model and show that in equilibrium an Open Source sector appears only after a proprietary sector. We also find conditions under which the model has a unique equilibrium, in which a proprietary and an Open Source sector coexist and compete in the short run, but the Open Source sector dominates the industry in the long run. We use our model to study whether patents are inefficient, and to explain firms' behavior in the software and the biomedical industry.