Abstract. We consider the problem of learning equilibria in a well known game theoretic traffic model due to Wardrop. We consider a distributed learning algorithm that we prove to converge to equilibria. The proof of convergence is based on a differential equation governing the global macroscopic evolution of the system, inferred from the local microscopic evolutions of agents. We prove that the differential equation converges with the help of Lyapunov techniques.
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 (weakly) converge 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.
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