Federated Learning (FL) is a distributed learning framework that can deal with the distributed issue in machine learning and still guarantee high learning performance. However, it is impractical that all users will sacrifice their resources to join the FL algorithm. This motivates us to study the incentive mechanism design for FL. In this paper, we consider a FL system that involves one base station (BS) and multiple mobile users. The mobile users use their own data to train the local machine learning model, and then send the trained models to the BS, which generates the initial model, collects local models and constructs the global model. Then, we formulate the incentive mechanism between the BS and mobile users as an auction game where the BS is an auctioneer and the mobile users are the sellers. In the proposed game, each mobile user submits its bids according to the minimal energy cost that the mobile users experiences in participating in FL. To decide winners in the auction and maximize social welfare, we propose the primal-dual greedy auction mechanism. The proposed mechanism can guarantee three economic properties, namely, truthfulness, individual rationality and efficiency. Finally, numerical results are shown to demonstrate the performance effectiveness of our proposed mechanism.
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