Upper Bounding the Price of Anarchy in Atomic Splittable Selfish Routing

Selfish behavior of nodes of a network such as sensors of a geographically distributed sensor network, each of which owned and operated by a different stakeholder may lead to a game theoretic setting called “selfish routing”. The fact that every node strictly aims at maximizing its own utility can cause degradations of social welfare. An issue of concern would be the quantitative measure of this inefficiency. We study the price of anarchy in selfish routing games, a quantitative measure of inefficiency of worst equilibrium of the game imposed by noncooperative behavior of players. For the most of this paper, we consider atomic models of selfish routing in which the network is a multicommodity flow network with multiple sources and sinks, and each player controls a considerable amount of the overall traffic. The price of anarchy for many variants of atomic splittable instances is not well understood, and upper bounding this parameter in presence of affine cost functions is the problems we tackle in this paper.