In this paper I study how innovation investment in a software duopoly is affected by the fact that one of the firms is, or might become Open Source. Firms can either be proprietary source (PS) or open source (OS) and have different initial technological levels. An OS firm is a for profit organization whose basic software is OS and it is distributed for free. The OS firm, however, is able to make profits from selling complementary software and, on the cost side, it receives development help from a community of users. I first compare a duopoly composed by two PS firms with a mixed duopoly of a PS and OS firm and I find that a PS duopoly might generate more innovation than a mixed duopoly if the initial technological gap between firms is small. However if this gap is large, a PS duopoly generates less innovation than a mixed duopoly. I then extend the setting to allow PS firms to switch to OS or to remain PS. A PS firm wants to become OS if it gets behind enough in the technological race against a competitor. I find that the outside option to become OS might soften competition on innovation since the technological leader prefers to reduce his innovation investment to avoid the OS switch of the follower. Therefore, although the switch to OS could generate higher investment levels ex-post it might generate lower investment ex-ante. In this context I find that a government subsidy to OS firms could be potentially harmful for innovation.