We study collaborative learning systems in which the participants are competitors who will defect from the system if they lose revenue by collaborating. As such, we frame the system as a duopoly of competitive firms who are each training machine learning models and selling their predictions to a market of consumers. We first examine a fully collaborative scheme in which both firms share their models with each other and show that this leads to a market collapse with the revenues of both firms going to zero. We next show that one-sided collaboration in which only the firm with the lower-quality model shares improves the revenue of both firms. Finally, we propose a more equitable, \emph{defection-free} scheme in which both firms share with each other while losing no revenue. We show that for a large range of starting conditions, our algorithm converges to the Nash bargaining solution, and we empirically verify our theory on computer vision datasets.