You Won the Battle. What about the War? A Model of Competition between Proprietary and Open Source Software

Although open source software has recently attracted a relevant body of economic literature, a formal treatment of the process of com- petition with its proprietary counterpart is still missing. Starting from an epidemic model of innovation di?usion, we try to ?ll this gap. We propose a model where the two competing technologies depend on dif- ferent factors, each one speci?c to its own mode of production (prof- its and developers’ motivations respectively), together with network e?ects and switching costs. As the speed of di?usion of these tech- nologies is crucial for the ?nal outcome, we endogenize the parame- ter in?uencing it across the population of adopters. We ?nd that an asymptotically stable equilibrium where both technologies coexist can always be present and, when the propagation coe?cient is endogenous, it coexists with winner–take–all solutions. Furthermore, an increase in the level of the switching costs for one technology increases the num- ber of its adopters, while reducing the number of the other one. If the negative network e?ects increase for one of the two technologies, then the equilibrium level of users of that technology decrease.