  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 engaged in 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, *defection-free* scheme in which both firms share
with each other while losing no revenue, and we show that our algorithm
converges to the Nash bargaining solution.
