A dynamic model of mixed duopolistic competition: open source vs. proprietary innovation

Abstract

Open source software development has been an interesting investment model of production and innovation in recent years, especially in the last few decades. Unlike the private investment model, open source innovators freely share the software that they have developed at their private expense. Also, open source development is usually subject to certain licenses, one of which being the General Public License (GPL), the most popular open source license. In this thesis, we study the competition dynamics between a proprietary firm and an open source firm, Windows and Linux, for instance. We model the the competition between such two firms by incorporating the nature of the GPL, investment opportunities by the proprietary firm, user developers who can invest in the open source development, and a ladder type technology. We use a two period dynamic mixed duopoly model, in which a profitmaximizing proprietary firm competes with a rival, the open source firm, which prices the product at zero, with the quality levels determining their relative positions over time. We ask the following questions. How does the existence of open source firm affect the investment and the pricing behavior of the proprietary firm? Does the social welfare increase with the existence of the open source development? How are the users/consumers affected from the open source firm being available? We also discuss the limitations of our model and possible extensions.