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.

翻译：我们研究一种协作学习系统，其中参与者是竞争对手，若因协作导致收益受损便会退出系统。为此，我们将系统建模为双寡头竞争企业，每家企业均致力于训练机器学习模型，并向消费者市场出售其预测结果。首先，我们考察一种完全协作方案，即两家企业相互共享模型，结果表明这会导致市场崩溃，两家企业的收益均降为零。接着，我们证明单向协作——即仅允许模型质量较低的企业共享模型——能够提升两家企业的收益。最后，我们提出一种更公平的*无背叛*方案，在该方案中两家企业相互共享模型且不会损失收益，并证明我们的算法收敛于纳什讨价还价解。