Technical Report: Coopetition in Heterogeneous Cross-Silo Federated Learning

In cross-silo federated learning (FL), companies collaboratively train a shared global model without sharing heterogeneous data. Prior related work focused on algorithm development to tackle data heterogeneity. However, the dual problem of coopetition, i.e., FL collaboration and market competition, remains under-explored. This paper studies the FL coopetition using a dynamic two-period game model. In period 1, an incumbent company trains a local model and provides model-based services at a chosen price to users. In period 2, an entrant company enters, and both companies decide whether to engage in FL collaboration and then compete in selling model-based services at different prices to users. Analyzing the two-period game is challenging due to data heterogeneity, and that the incumbent's period one pricing has a temporal impact on coopetition in period 2, resulting in a non-concave problem. To address this issue, we decompose the problem into several concave sub-problems and develop an algorithm that achieves a global optimum. Numerical results on three public datasets show two interesting insights. First, FL training brings model performance gain as well as competition loss, and collaboration occurs only when the performance gain outweighs the loss. Second, data heterogeneity can incentivize the incumbent to limit market penetration in period 1 and promote price competition in period 2.