  We consider a discrete-time nonatomic routing game with variable demand and
uncertain costs. Given a routing network with single origin and destination,
the cost function of each edge depends on some uncertain persistent state
parameter. At every period, a random traffic demand is routed through the
network according to a Wardrop equilibrium. The realized costs are publicly
observed and the public Bayesian belief about the state parameter is updated.
We say that there is strong learning when beliefs converge to the truth and
weak learning when the equilibrium flow converges to the complete-information
flow. We characterize the networks for which learning occurs. We prove that
these networks have a series-parallel structure and provide a counterexample to
show that learning may fail in non-series-parallel networks.
