RATE: Game-Theoretic Design of Sustainable Incentive Mechanism for Federated Learning

Although federated learning (FL) enables collaborative training across multiple decentralized devices, strategic clients may be reluctant to participate in FL unless sufficient incentives are available. Existing researches predominantly emphasize short-term incentives, while FL model training is typically a long-term process, and malicious clients may exhibit dishonest behavior during local training. Although designing a long-term incentive mechanism is crucial for FL, this task is challenging due to the heterogeneous nature of FL and the limitations of imperfect system monitoring. To this end, this article designs the first sustainable incentive mechanism for FL called RATE, which aims to incentivize clients to continuously contribute more high-quality data. Specifically, by modeling the competition and cooperation relationship between servers and clients as a multiserver multiclient Stackelberg game, we prove the existence and uniqueness of the Stackelberg equilibrium (SE), and derive the unique SE through the cautious calculation of designed algorithms. Since the derived SE may not be optimal, we further utilize reputation to measure the long-term contribution of clients and build a function between their revenues and reputations to ensure the optimal revenue allocation, thereby maximizing the social welfare of RATE. Extensive experiments on both synthetic and real data sets demonstrate the superiority of RATE. Compared to the state-of-the-art baselines, RATE increases the total utility of the servers by up to 20%, reduces the reputation of malicious clients by up to 90%, and improves the average test accuracy overall.