Braess' paradox: A cooperative game-theoretic point of view

Mauro Passacantando, Giorgio Gnecco, Yuval Hadas, Marcello Sanguineti

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

Braess' paradox is a classical result in the theory of congestion games. It motivates theoretically why adding a resource (e.g., an arc) to a network may sometimes worsen, rather than improve, the overall network performance. Differently from previous literature, which studies Braess' paradox in a non-cooperative game-theoretic setting, in this work, a framework is proposed to investigate its occurrence by exploiting cooperative games with transferable utility (TU games) on networks. In this way, instead of focusing on the marginal contribution to the network utility provided by the insertion of an arc when a single initial scenario is considered, the arc average marginal utility with respect to various initial scenarios, that is, its Shapley value in a suitably-defined TU game, is evaluated. It is shown that, for choices of the utility function of the TU game modeling congestion, there are cases for which the Shapley value associated with an arc is negative, meaning that its average marginal contribution to the network utility is negative.

Original languageEnglish
Pages (from-to)264-283
Number of pages20
JournalNetworks
Volume78
Issue number3
DOIs
StatePublished - Oct 2021

Bibliographical note

Publisher Copyright:
© 2021 Wiley Periodicals LLC.

Funding

M. Passacantando, G. Gnecco, and M. Sanguineti are members of the Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA—National Group for Mathematical Analysis, Probability and their Applications) of the Istituto Nazionale di Alta Matematica (INdAM—National Institute of Higher Mathematics). M. Sanguineti is Research Associate at INM (Institute for Marine Engineering) of CNR (National Research Council of Italy) under the Project PDGP 2018/20 DIT.AD016.001 “Technologies for Smart Communities”, Affiliated Researcher at the Italian Institute of Technology (IIT) for the research line Advanced Robotics, and Visiting Professor at IMT - School for Advanced Studies – AXES Research Unit, Lucca, Italy.

FundersFunder number
INdAM—National Institute of Higher Mathematics
Istituto Nazionale di Alta Matematica "Francesco Severi"
Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni
Scuola IMT Alti Studi Lucca
Consiglio Nazionale delle RicerchePDGP 2018/20 DIT.AD016.001
Istituto Italiano di Tecnologia

    Keywords

    • Braess' paradox
    • TU games
    • system optimum
    • traffic assignment
    • transportation networks
    • user equilibrium

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