Optimal Firm Contributions to Open Source Software

Abstract

This paper examines open source software development in a competitive environment. The quality of open source software improves over time based upon contributions by firms and users. A firm's decision to contribute is interesting because it also augments competitors' software quality in future periods subject to compatibility considerations with their existing software. A differential game model is developed to understand why firms are increasingly involved in open source software development by determining the optimal contributions and software quality over time. We obtain a closed-loop Nash equilibrium solution. Examples are given to derive insights from this model.

Keywords: Open sourcd software, dynamic games, game theory, differential games, optimal control, close-loop Nash equilibrium, software quality

JEL Classification: C61, D42, M00