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This paper presents a game theoretic framework for participation and free-riding in federated learning (FL), and determines the Nash equilibrium strategies when FL is executed over wireless links. To support spectrum sensing for NextG communications, FL is used by clients, namely spectrum sensors with limited training datasets and computation resources, to train a wireless signal classifier while preserving privacy. In FL, a client may be free-riding, i.e., it does not participate in FL model updates, if the computation and transmission cost for FL participation is high, and receives the global model (learned by other clients) without incurring a cost. However, the free-riding behavior may potentially decrease the global accuracy due to lack of contribution to global model learning. This tradeoff leads to a non-cooperative game where each client aims to individually maximize its utility as the difference between the global model accuracy and the cost of FL participation. The Nash equilibrium strategies are derived for free-riding probabilities such that no client can unilaterally increase its utility given the strategies of its opponents remain the same. The free-riding probability increases with the FL participation cost and the number of clients, and a significant optimality gap exists in Nash equilibrium with respect to the joint optimization for all clients. The optimality gap increases with the number of clients and the maximum gap is evaluated as a function of the cost. These results quantify the impact of free-riding on the resilience of FL in NextG networks and indicate operational modes for FL participation.

Free-Rider Games for Federated Learning with Selfish Clients in NextG Wireless Networks