Industry equilibrium with open-source and proprietary firms

We present a model of industry equilibrium to study the coexistence of open-source and proprietary firms. Two novel aspects of the model are (i) participation in open source arises as the optimal decision of profit-maximizing firms, and (ii) open-source and proprietary firms may (or may not) coexist in equilibrium. Firms decide their type and investment in R&D, and sell packages composed of a primary good and a complementary private good. Open-source firms share their technological advances on the primary good, whereas proprietary firms keep their innovations private. The main contribution of the paper is to determine conditions under which open-source and proprietary firms coexist in equilibrium. Interestingly, this equilibrium is characterized by an asymmetric market structure, with few large proprietary firms and many small open-source firms. We also study the limiting economy and present conditions under which large numbers favor cooperation in R&D.