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Weighted Congestion Games: The Price of Anarchy, Universal Worst-Case Examples, and Tightness

Weighted Congestion Games: The Price of Anarchy, Universal Worst-Case Examples, and Tightness Weighted Congestion Games: The Price of Anarchy, Universal Worst-Case Examples, and Tightness KSHIPRA BHAWALKAR, Stanford University MARTIN GAIRING, University of Liverpool TIM ROUGHGARDEN, Stanford University We characterize the Price of Anarchy (POA) in weighted congestion games, as a function of the allowable resource cost functions. Our results provide as thorough an understanding of this quantity as is already known for nonatomic and unweighted congestion games, and take the form of universal (cost function-independent) worst-case examples. One noteworthy by-product of our proofs is the fact that weighted congestion games are "tight," which implies that the worst-case price of anarchy with respect to pure Nash equilibria, mixed Nash equilibria, correlated equilibria, and coarse correlated equilibria are always equal (under mild conditions on the allowable cost functions). Another is the fact that, like nonatomic but unlike atomic (unweighted) congestion games, weighted congestion games with trivial structure already realize the worst-case POA, at least for polynomial cost functions. We also prove a new result about unweighted congestion games: the worst-case price of anarchy in symmetric games is as large as in their more general asymmetric counterparts. Categories and Subject Descriptors: F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems General http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Economics and Computation Association for Computing Machinery

Weighted Congestion Games: The Price of Anarchy, Universal Worst-Case Examples, and Tightness

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Publisher
Association for Computing Machinery
Copyright
Copyright © 2014 by ACM Inc.
ISSN
2167-8375
DOI
10.1145/2629666
Publisher site
See Article on Publisher Site

Abstract

Weighted Congestion Games: The Price of Anarchy, Universal Worst-Case Examples, and Tightness KSHIPRA BHAWALKAR, Stanford University MARTIN GAIRING, University of Liverpool TIM ROUGHGARDEN, Stanford University We characterize the Price of Anarchy (POA) in weighted congestion games, as a function of the allowable resource cost functions. Our results provide as thorough an understanding of this quantity as is already known for nonatomic and unweighted congestion games, and take the form of universal (cost function-independent) worst-case examples. One noteworthy by-product of our proofs is the fact that weighted congestion games are "tight," which implies that the worst-case price of anarchy with respect to pure Nash equilibria, mixed Nash equilibria, correlated equilibria, and coarse correlated equilibria are always equal (under mild conditions on the allowable cost functions). Another is the fact that, like nonatomic but unlike atomic (unweighted) congestion games, weighted congestion games with trivial structure already realize the worst-case POA, at least for polynomial cost functions. We also prove a new result about unweighted congestion games: the worst-case price of anarchy in symmetric games is as large as in their more general asymmetric counterparts. Categories and Subject Descriptors: F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumerical Algorithms and Problems General

Journal

ACM Transactions on Economics and ComputationAssociation for Computing Machinery

Published: Oct 28, 2014

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