Evolutionary dynamics and potential games in non-cooperative routing

We consider a routing problem in a network with a general topology. Considering a link cost which is linear in the link flow, we obtain a unique Nash equilibrium and show that the non-cooperative game can be expressed as a potential game. We establish various convergence and stability properties of of the equilibrium related to the routing problem being a potential game. We then consider the routing problem in the framework of a population game and study the evolution of the size of the populations when the replicator dynamics is used.