The price of atomic selfish ring routing

We study selfish routing in ring networks with respect to minimizing the maximum latency. Our main result is an establishment of constant bounds on the price of stability (PoS) for routing unsplittable flows with linear latency. We show that the PoS is at most 6.83, which reduces to 4.57 when the linear latency functions are homogeneous. We also show the existence of a (54,1)-approximate Nash equilibrium. Additionally we address some algorithmic issues for computing an approximate Nash equilibrium.