RAIM: three-stage stackelberg game for hierarchical federated learning with reputation-aware incentive mechanism

Hierarchical Federated Learning (HFL) significantly enhances communication efficiency and device participation, while improving personalized learning outcomes. In this framework, incentive mechanisms are crucial as they ensure that devices actively participate and make genuine contributions. However, existing incentive mechanisms struggle to effectively address the issue of unreliable devices, which may negatively impact model training due to malicious behavior or faults, leading to low-quality updates or even failure of the global model. Additionally, participants' strategic behaviors and device heterogeneity can further diminish the effectiveness of these mechanisms. To tackle these challenges, this paper proposes a Reputation-Aware Incentive Mechanism (RAIM) aimed at optimizing node cooperation within HFL and enhancing overall system performance. Specifically, we first evaluate the reputation value of end devices based on their training quality and historical records, which can identify and defend against malicious data attacks. Participants' reputations are maintained through a consortium blockchain, thereby ensuring transparency and fairness. Next, we model the interaction of HFL as a three-stage Stackelberg game to address hierarchical decision-making processes, and also prove that there is a unique Stackelberg equilibrium, derived through cautiously proposed algorithms. Since the existing equilibrium may not be optimal, we further design optimal server selection algorithm to motivate high-reputation and low-cost devices to participate in training, while maximizing both system performance and social utility. Finally, extensive experiments using both synthetic and real datasets show that our RAIM outperforms state-of-the-art baseline methods.