Coexistence and Market Tipping in a Diffusion Model of Open Source vs. Proprietary Software

A large number of studies has been canvassed by the growing rates of diffusion of Open Source Software. However, a formal analysis of the process of competition between open-source and proprietary software is still missing. We propose an epidemic model of innovation diffusion to deal with the different factors (profits for proprietary software and developers’ motivations for open–source software) upon which such a process of competition ultimately depends Moreover, we add network effects and switching costs, together with the endogenisation of the parameters of the speed of diffusion influencing the final outcome. We show the conditions for an asymptotically stable equilibrium to exist, where both softwares coexist. When the propagation coefficient is endogenous, winner–take–all solutions are also likely. Furthermore, an increase in the level of the switching costs for one software increases the number of its adopters, while reducing that of the other one. If the negative network effects increase for one of the two softwares, then the equilibrium level of users of that software decreases