Worst-case nash equilibria in restricted routing

Abstract

We study a restricted related model of the network routing problem. There are m parallel links with possibly different speeds, between a source and a sink. And there are n users, and each user i has a traffic of weight w i to assign to one of the links from a subset of all the links, named his/her allowable set. We analyze the Price of Anarchy (denoted by PoA) of the system, which is the ratio of the maximum delay in the worst-case Nash equilibrium and in an optimal solution. In order to better understand this model, we introduce a parameter λ for the system, and define an instance to be λ-good if for every user, there exist a link with speed at least in his/her allowable set. In this paper, we prove that for λ-good instances, the Price of Anarchy is . We also show an important application of our result in coordination mechanism design for task scheduling game. We propose a new coordination mechanism, Group-Makespan, for unrelated selfish task scheduling game. Our new mechanism ensures the existence of pure Nash equilibrium and its PoA is . This result improves the best known result of O(log2 m) by Azar, Jain and Mirrokni in [2]. © 2008 Springer Berlin Heidelberg.