Distributed learning of equilibria in a routing game

We focus on the problem of learning equilibria in a particular routing game similar to the Wardrop traffic model. We describe a routing game played by a large number of players and present a distributed learning algorithm that we prove to converge weakly to equilibria for the system. The proof of convergence is based on a differential equation governing the global evolution of the system that is inferred from all the local evolutions of the agents in play. We prove that the differential equation converges with the help of Lyapunov techniques.