A Pricing Game for Federated Learning Supporting Lightweight Local Model Training
Fengsen Tian, Mingzi Wang, Yu Zhang, Guoqiang Deng, Lingyu Liang, Xinglin Zhang · IEEE Transactions on Mobile Computing · 2025
The pervasive distribution of data across clients with privacy concerns and heterogeneous performance in edge networks presents a significant opportunity to enhance AI model performance. Federated learning (FL) enables a model owner (MO) to recruit these clients, offering compensation for their contributions, and to improve model quality by aggregating knowledge from their locally trained models. However, several challenges arise in this process. Clients may decline participation if they do not achieve positive utility. Moreover, due to constraints in memory, computing, and communication resources, some clients can only train lightweight models that represent partial versions of the global model. Importantly, the MO's pricing for client contributions and the proportions of local model training are interdependent, collectively influencing client utilities and participation decisions. To address these challenges, we first model the utility functions of both the MO and the clients, accommodating the support for lightweight local models. We then formulate their interactions as a Stackelberg game and theoretically prove the existence of a Nash equilibrium. Based on this equilibrium, we derive optimal collaboration strategies for both the MO and the clients. Additionally, we design an efficient approximation algorithm to enable the MO to maximize its utility by selecting suitable clients to participate in FL. Finally, extensive experiments validate our theoretical findings, demonstrating the superior performance and effectiveness of the proposed algorithms