Cost-sharing in generalised selfish routing

© Springer International Publishing AG 2017. We study a generalisation of atomic selfish routing games where each player may control multiple flows which she routes seek-ing to minimise their aggregate cost. Such games emerge in various set-tings, such as traffic routing in road networks by competing ride-sharing applications or packet routing in communication networks by competing service providers who seek to optimise the quality of service of their cus-tomers. We study the existence of pure Nash equilibria in the induced games and we exhibit a separation from the single-commodity per player model by proving that the Shapley value is the only cost-sharing method that guarantees it. We also prove that the price of anarchy and price of stability is no larger than in the single-commodity model for general cost-sharing methods and general classes of convex cost functions. We close by giving results on the existence of pure Nash equilibria of a splittable variant of our model