Preliminary draft

Abstract: In this paper, we study oligopolistic competition between closed and open source softwares. By intersecting existing economic contributions on open source, we propose a two stage game with perfect information and product di¤eretiation in which producers \u85rstly set softwares quality, then they determine prices (constrained at zero for open source programs). In doing this, we explicitly model lock-in e¤ects, network externality componentsof software quality as well as knowledge accumulation in software use and implementation. With respect to a monopolistic benchmark case, we argue that in duopoly a pro-prietary sofware producer facing an open source software will reduce its selling price whether: (i) its network of users is larger than open sources one and its consumers are largely experienced on its program, (ii) it has a small network of un-skilled consumers. In opposition, after open source softwares emergence, proprietary software price does augment if proprietary software users form a large, but poorly skilled network. Fur-thermore, we show that, in all above cases, proprietary software quality increases because of the existence of a open source alternative to a previouisly monopolistic program. Finally, by modeling knowledge accumulation processes through di¤erence equa-tions, we show that the ratio between closed and open source programsopportunity costs of software learning and deployment plays a crucial role in shaping market out-comes. Until an open source software remains too complex and technical for unskilled or time-scarse users, a shared market solution in which both softwares are adopted is predicted. In contrast, if opportunity costs in learning and understanding open source programs are remarkably low, or at least equal to opportunity costs of a closed source software, then a open source dominance outcome (i.e. all software are open ones) phases out.