Selfish unsplittable flows

On the other hand, we prove that any weighted network congestion game with linear edge delays admits a pure Nash equilibrium that can be found in pseudo-polynomial time. Finally, we consider the family of ℓ-layered networks and give a surprising answer to the question above: the price of anarchy of any weighted congestion game in a ℓ-layered network with m edges and edge delays equal to the loads is Θ(logm/loglogm).