  We study learning dynamics induced by myopic travelers who repeatedly play a
routing game on a transportation network with an unknown state. The state
impacts cost functions of one or more edges of the network. In each stage,
travelers choose their routes according to Wardrop equilibrium based on public
belief of the state. This belief is broadcast by an information system that
observes the edge loads and realized costs on the used edges, and performs a
Bayesian update to the prior stage's belief. We show that the sequence of
public beliefs and edge load vectors generated by the repeated play converge
almost surely. In any rest point, travelers have no incentive to deviate from
the chosen routes and accurately learn the true costs on the used edges.
However, the costs on edges that are not used may not be accurately learned.
Thus, learning can be incomplete in that the edge load vectors at rest point
and complete information equilibrium can be different. We present some
conditions for complete learning and illustrate situations when such an outcome
is not guaranteed.
