We consider a hierarchical network model with multiple links, a single
service provider, and a large number of multiple classes of users, who
enter and exit the network at possibly different node-pairs. Each user
has a fixed route, is charged a fixed price per unit of bandwidth used
on each link in its route, and chooses the level of its flow by
maximizing an objective function that captures a trade-off between the
disutility of the payment to the service provider and congestion costs
on the links the user transmits, and the utility of its flow. The
service provider, on the other hand, wishes to maximize the total
revenue it collects. Viewing this as a large-scale Stackelberg game,
with a single leader (the service provider, who sets the price) and a
large number of Nash followers (the users), we will discuss the
solution to this network game, including the limiting case where the
number of users in each class grows without bound, while the capacity
is increased in proportion to the number of users. The asymptotic
results reveal a number of interesting properties of the equilibrium,
and answer the question of whether and when the service provider has
the incentive to add additional capacity to the network in response to
an increase in the number of users on a particular link.  Extensions
to to the case of multiple service providers and differential pricing
will also be discussed.