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 language | English |
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Pages (from-to) | 264-283 |
Number of pages | 20 |
Journal | Networks |
Volume | 78 |
Issue number | 3 |
DOIs | |
State | Published - 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.
Funders | Funder number |
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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 Ricerche | PDGP 2018/20 DIT.AD016.001 |
Istituto Italiano di Tecnologia |
Keywords
- Braess' paradox
- TU games
- system optimum
- traffic assignment
- transportation networks
- user equilibrium