  Federated learning protects users' data privacy through sharing users' local
model parameters (instead of raw data) with a server. However, when massive
users train a large machine learning model through federated learning, the
dynamically varying and often heavy communication overhead can put significant
pressure on the network operator. The operator may choose to dynamically change
the network prices in response, which will eventually affect the payoffs of the
server and users. This paper considers the under-explored yet important issue
of the joint design of participation incentives (for encouraging users'
contribution to federated learning) and network pricing (for managing network
resources). Due to heterogeneous users' private information and
multi-dimensional decisions, the optimization problems in Stage I of
multi-stage games are non-convex. Nevertheless, we are able to analytically
derive the corresponding optimal contract and pricing mechanism through proper
transformations of constraints, variables, and functions, under both vertical
and horizontal interaction structures of the participants. We show that the
vertical structure is better than the horizontal one, as it avoids the
interests misalignment between the server and the network operator. Numerical
results based on real-world datasets show that our proposed mechanisms decrease
server's cost by up to 24.87% comparing with the state-of-the-art benchmarks.
