  Federated Learning (FL) aims to foster collaboration among a population of
clients to improve the accuracy of machine learning without directly sharing
local data. Although there has been rich literature on designing federated
learning algorithms, most prior works implicitly assume that all clients are
willing to participate in a FL scheme. In practice, clients may not benefit
from joining in FL, especially in light of potential costs related to issues
such as privacy and computation. In this work, we study the clients' incentives
in federated learning to help the service provider design better solutions and
ensure clients make better decisions. We are the first to model clients'
behaviors in FL as a network effects game, where each client's benefit depends
on other clients who also join the network. Using this setup we analyze the
dynamics of clients' participation and characterize the equilibrium, where no
client has incentives to alter their decision. Specifically, we show that
dynamics in the population naturally converge to equilibrium without needing
explicit interventions. Finally, we provide a cost-efficient payment scheme
that incentivizes clients to reach a desired equilibrium when the initial
network is empty.
