A Dynamic Model of Mixed Duopolistic Competition: Open Source vs. Proprietary Innovation

Abstract

We model the competition between a proprietary firm and an open source rival, 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 profit-maximizing 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 analyze how the existence of open source firm affects the investment and the pricing behavior of the proprietary firm. We also study the welfare implications of the existence of the open source rival. We find that, under some conditions, the existence of an open source rival may decrease the total welfare.