Learning dynamics in stochastic routing games

We consider a repeated nonatomic network routing game where a large number of risk-neutral users are unsure about the edge latency functions and learn about them using past travel experience. We assume that the network has affine stochastic edge latency functions with unknown slope. We consider a simple process of learning where agents share common observations of travel times, estimate the unknown edge slope parameters via ordinary least squares and, at every step, dispatch their traffic demand over the network according to the Wardrop equilibrium computed using mean latency functions with most recent estimates. We prove that under this learning dynamics, the flow vector in the network converges almost surely to the full information Wardrop equilibrium. Moreover, the slope parameters of all the edges used in the full information Wardrop equilibrium are learned almost surely in the limit.