Article

The Structure and Complexity of Nash Equilibria for a Selfish Routing Game

Authors:

Dimitris Fotakis,

Spyros C. Kontogiannis,

Elias Koutsoupias,

Marios Mavronicolas,

Paul G. SpirakisAuthors Info & Claims

ICALP '02: Proceedings of the 29th International Colloquium on Automata, Languages and Programming

Pages 123 - 134

Published: 08 July 2002 Publication History

Abstract

In this work, we study the combinatorial structure and the computational complexity of Nash equilibria for a certain game that models selfish routing over a network consisting of m parallel links. We assume a collection of n users, each employing a mixed strategy, which is a probability distribution over links, to control the routing of its own assigned traffic. In a Nash equilibrium, each user selfishly routes its traffic on those links that minimize its expected latency cost, given the network congestion caused by the other users. The social cost of a Nash equilibrium is the expectation, over all random choices of the users, of the maximum, over all links, latency through a link.We embark on a systematic study of several algorithmic problems related to the computation of Nash equilibria for the selfish routing game we consider. In a nutshell, these problems relate to deciding the existence of a Nash equilibrium, constructing a Nash equilibrium with given support characteristics, constructing the worst Nash equilibrium (the one with maximum social cost), constructing the best Nash equilibrium (the one with minimum social cost), or computing the social cost of a (given) Nash equilibrium. Our work provides a comprehensive collection of efficient algorithms, hardness results (both as NP-hardness and #P-completeness results), and structural results for these algorithmic problems. Our results span and contrast a wide range of assumptions on the syntax of the Nash equilibria and on the parameters of the system.

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cover image Guide Proceedings

ICALP '02: Proceedings of the 29th International Colloquium on Automata, Languages and Programming

July 2002

1065 pages

ISBN:3540438645

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 08 July 2002

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Mustafa SNazir BHayat AKhan AMadani S(2015)Resource management in cloud computingComputers and Electrical Engineering10.1016/j.compeleceng.2015.07.02147:C(186-203)Online publication date: 1-Oct-2015
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