Efficiency of Atomic Splittable Selfish Routing with Polynomial Cost Functions

Abstract

Previous works on the inefficiency of selfish routing have focused on the Wardropian traffic equilibria with an infinite number of infinitesimal players, each controlling a negligible fraction of the overall traffic, but only very limited pseudo-approximation results have been obtained for the atomic selfish routing game with a finite number of players. In this note we examine the price of anarchy of selfish routing with atomic Cournot–Nash players, each controlling a strictly positive splittable amount of flow. We obtain an upper bound of the inefficiency of equilibria with polynomial cost functions, and show that the bound is 1 or there is no efficiency loss when there is only one player, and the bound reduces to the result established in the literature when there are an infinite number of infinitesimal players.