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Hierarchical Federated Learning (HFL) is a distributed machine learningparadigm tailored for multi-tiered computation architectures, which supportsmassive access of devices' models simultaneously. To enable efficient HFL, itis crucial to design suitable incentive mechanisms to ensure that devicesactively participate in local training. However, there are few studies onincentive mechanism design for HFL. In this paper, we design two-levelincentive mechanisms for the HFL with a two-tiered computing structure toencourage the participation of entities in each tier in the HFL training. Inthe lower-level game, we propose a coalition formation game to joint optimizethe edge association and bandwidth allocation problem, and obtain efficientcoalition partitions by the proposed preference rule, which can be proven to bestable by exact potential game. In the upper-level game, we design theStackelberg game algorithm, which not only determines the optimal number ofedge aggregations for edge servers to maximize their utility, but also optimizethe unit reward provided for the edge aggregation performance to ensure theinterests of cloud servers. Furthermore, numerical results indicate that theproposed algorithms can achieve better performance than the benchmark schemes.

Design of Two-Level Incentive Mechanisms for Hierarchical Federated Learning