  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.
