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Matroids Are Immune to Braess’ Paradox

Author

Listed:
  • Satoru Fujishige

    (Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606, Japan)

  • Michel X. Goemans

    (Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • Tobias Harks

    (Institute of Mathematics, University of Augsburg, 86135 Augsburg, Germany)

  • Britta Peis

    (School of Business and Economics, RWTH Aachen University, 52072 Aachen, Germany)

  • Rico Zenklusen

    (Department of Mathematics, ETH Zürich, 8092 Zürich, Switzerland; Department of Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, Maryland 21218)

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 separable optimization problems over polymatroid base polyhedra, which may be of independent interest.

Suggested Citation

  • Satoru Fujishige & Michel X. Goemans & Tobias Harks & Britta Peis & Rico Zenklusen, 2017. "Matroids Are Immune to Braess’ Paradox," Mathematics of Operations Research, INFORMS, vol. 42(3), pages 745-761, August.
    • Handle: RePEc:inm:ormoor:v:42:y:2017:i:3:p:745-761
    DOI: 10.1287/moor.2016.0825
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    References listed on IDEAS

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