Tight bounds for worst-case equilibria
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
The Structure and Complexity of Nash Equilibria for a Selfish Routing Game
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Computing Nash equilibria for scheduling on restricted parallel links
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Tradeoffs in worst-case equilibria
Theoretical Computer Science - Approximation and online algorithms
Algorithmica
(Almost) optimal coordination mechanisms for unrelated machine scheduling
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Coordination mechanisms for selfish scheduling
WINE'05 Proceedings of the First international conference on Internet and Network Economics
Local search performance guarantees for restricted related parallel machine scheduling
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
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We study a restricted related model of the network routingproblem. There are m parallel links with possibly different speeds,between a source and a sink. And there are n users, and each user ihas a traffic of weight w i to assign to one of the links from asubset of all the links, named his/her allowable set. We analyzethe Price of Anarchy (denoted by PoA) of the system, which is theratio of the maximum delay in the worst-case Nash equilibrium andin an optimal solution. In order to better understand this model,we introduce a parameter λ for the system, and define aninstance to be λ-good if for every user, there exist a linkwith speed at least $\frac{s_{max}}{\lambda}$ in his/her allowableset. In this paper, we prove that for λ-good instances, thePrice of Anarchy is $ \Theta \big( \min\{\frac{\log \lambda m}{\log\log \lambda m}, m\}\big)$. We also show an important applicationof our result in coordination mechanism design for task schedulinggame. We propose a new coordination mechanism, Group-Makespan, forunrelated selfish task scheduling game. Our new mechanism ensuresthe existence of pure Nash equilibrium and its PoA is $O\big(\frac{\log^2 m}{\log \log m}\big)$. This result improves thebest known result of O(log2 m) by Azar, Jain and Mirrokni in[2].