DUOPOLY OF LINUX AND MICROSOFT AS COMPETING SERVER OPERATING SYSTEMS

The paper is motivated by Microsoft Windows and Linux competition at the server operating systems market. Microsoft/Linux mixed duopoly dynamics is analyzed using optimal control mathematical model where Microsoft is considered as a profit-maximizing competitor while Linux as an open source software project is assumed non-for-profit. Previous studies of mixed duopolies were static except the paper by Cassadeus-Masanell and Ghemawat (2006) where a dynamic mixed duopoly was presented and applied to Windows/Linux competition investigation. This paper presents some extensions and modifications of Cassadeus-Masanell and Ghemawat‘s model. Cassadeus-Masanell and Ghemawat assumed that at the demand side of the model in each period of time a new cohort of potential users enters the market, and the size of this cohort does not depend on time. We here assume that the cohort size is increasing exponentially. It is important that the demand side is learning and it affects the cost side. Another addition to the Cassadeus-Masanell and Ghemawat‘s model is that the cost investments in learning are endogenous. The conditions when Linux And Windows coexist at the market and when Linux is pushed out by Windows and vice versa are obtained and discussed. The special attention in the model presented is given to a piracy of Windows and strategic contribution to Linux issues which for the first time were discussed also by Cassadeus-Masanell and Ghemawat (2006).