Defection-Free Collaboration between Competitors in a Learning System

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.