Matroids Are Immune to Braess’ Paradox
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1504.07545.pdf
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Author(s)
Fujishige, Satoru
Harks, Tobias
Peis, Britta
Zenklusen, Rico
Goemans, Michel X
Date Issued
February 2017
Journal
Mathematics of Operations Research
Publisher
Institute for Operations Research and the Management Sciences (INFORMS)
Citation
Fujishige, Satoru et al. “Matroids Are Immune to Braess’ Paradox.” Mathematics of Operations Research 42, 3 (August 2017): 745–761 © 2017 INFORMS
Version
Author's final manuscript
Abstract
The famous Braess paradox describes the counterintuitive phenomenon in which, in certain settings, an increase of resources, such as a new road built within a congested network, may in fact lead to larger costs for the players in an equilibrium. In this paper, we consider general nonatomic congestion games and give a characterization of the combinatorial property of strategy spaces for which the Braess paradox does not occur. In short, matroid bases are precisely the required structure. We prove this characterization by two novel sensitivity results for convex separabl e optimization problems over polymatroid base polyhedra, which may be of independent interest. Keywords: nonatomic congestion games; Braess’ paradox; matroids; polymatroids
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1287/MOOR.2016.0825
