Three-Stage Stackelberg Game-Based Federated Learning With Wireless Power Transfer

Federated Learning (FL) enhances data privacy for End Equipment Workers (EWs) by enabling the sharing of model parameters instead of raw data. However, energy constraints and individual self-interest may discourage EWs from participating or slow down training, ultimately affecting the performance of the global FL model. To address these challenges, we propose a three-stage Stackelberg game-based framework that leverages wireless power to incentivize participation while ensuring the successful completion of FL tasks. In this framework, the Base Station (BS) publishes FL task and seeks to obtain an improved global model at a reduced cost. EWs train local models, aiming to maximize their payments while minimizing energy consumption. Meanwhile, the Charging Service Provider (CSP) supplies energy to EWs via Wireless Power Transfer (WPT) during model training and uploading, charging appropriate fees for the service. We employ the backward induction method to analyze the proposed game problem, proving the existence of a unique Stackelberg equilibrium and Nash equilibrium. Furthermore, we propose the Trust Region Method (TRM) to solve the unit payment strategy problem of BS. Extensive simulations validate that our method consistently outperforms benchmark schemes, achieving higher average utility across a wide range of scenarios.