IDEAS home Printed from https://ideas.repec.org/a/eee/mateco/v86y2020icp15-23.html
   My bibliography  Save this article

Pathwise smooth splittable congestion games and inefficiency

Author

Listed:
  • Raimondo, Roberto

Abstract

Very recently the inefficiency of Nash equilibria has been analyzed in the context of SplittableCongestionGames. These games are like the congestion games but allow the players to use convex combinations of subsets of resources. A new notion has been introduced in order to give bounds on the inefficiency or Price of Anarchy; such a notion has been termed the local smoothness. We present a unified framework where local smoothness and smoothness, a previously introduced notion, are presented as particular cases of a more general approach which we term pathwise smoothness. Such an approach is based partially on the Hadamard’s Lemma, which shows that it is possible to present any function, linear or not, by means of families of linear functions.

Suggested Citation

  • Raimondo, Roberto, 2020. "Pathwise smooth splittable congestion games and inefficiency," Journal of Mathematical Economics, Elsevier, vol. 86(C), pages 15-23.
    • Handle: RePEc:eee:mateco:v:86:y:2020:i:c:p:15-23
    DOI: 10.1016/j.jmateco.2019.10.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304406819301089
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmateco.2019.10.006?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Roberto Cominetti & José R. Correa & Nicolás E. Stier-Moses, 2009. "The Impact of Oligopolistic Competition in Networks," Operations Research, INFORMS, vol. 57(6), pages 1421-1437, December.
    2. Roughgarden, Tim & Tardos, Eva, 2004. "Bounding the inefficiency of equilibria in nonatomic congestion games," Games and Economic Behavior, Elsevier, vol. 47(2), pages 389-403, May.
    3. Roughgarden, Tim & Schoppmann, Florian, 2015. "Local smoothness and the price of anarchy in splittable congestion games," Journal of Economic Theory, Elsevier, vol. 156(C), pages 317-342.
    4. Blume, Lawrence & Easley, David & Kleinberg, Jon & Kleinberg, Robert & Tardos, Éva, 2015. "Introduction to computer science and economic theory," Journal of Economic Theory, Elsevier, vol. 156(C), pages 1-13.
    5. José R. Correa & Andreas S. Schulz & Nicolás E. Stier-Moses, 2004. "Selfish Routing in Capacitated Networks," Mathematics of Operations Research, INFORMS, vol. 29(4), pages 961-976, November.
    6. Pradeep Dubey, 1986. "Inefficiency of Nash Equilibria," Mathematics of Operations Research, INFORMS, vol. 11(1), pages 1-8, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Feng, Zengzhe & Gao, Ziyou & Sun, Huijun, 2014. "Bounding the inefficiency of atomic splittable selfish traffic equilibria with elastic demands," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 63(C), pages 31-43.
    2. Roberto Cominetti & José R. Correa & Nicolás E. Stier-Moses, 2009. "The Impact of Oligopolistic Competition in Networks," Operations Research, INFORMS, vol. 57(6), pages 1421-1437, December.
    3. Naimzada, A.K. & Raimondo, Roberto, 2018. "Heterogeneity and chaos in congestion games," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 278-291.
    4. Hota, Ashish R. & Garg, Siddharth & Sundaram, Shreyas, 2016. "Fragility of the commons under prospect-theoretic risk attitudes," Games and Economic Behavior, Elsevier, vol. 98(C), pages 135-164.
    5. Roughgarden, Tim & Schoppmann, Florian, 2015. "Local smoothness and the price of anarchy in splittable congestion games," Journal of Economic Theory, Elsevier, vol. 156(C), pages 317-342.
    6. 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.
    7. Correa, José & Hoeksma, Ruben & Schröder, Marc, 2019. "Network congestion games are robust to variable demand," Transportation Research Part B: Methodological, Elsevier, vol. 119(C), pages 69-78.
    8. Parilina, Elena & Sedakov, Artem & Zaccour, Georges, 2017. "Price of anarchy in a linear-state stochastic dynamic game," European Journal of Operational Research, Elsevier, vol. 258(2), pages 790-800.
    9. Vincenzo Bonifaci & Tobias Harks & Guido Schäfer, 2010. "Stackelberg Routing in Arbitrary Networks," Mathematics of Operations Research, INFORMS, vol. 35(2), pages 330-346, May.
    10. José R. Correa & Nicolás Figueroa & Nicolás E. Stier-Moses, 2008. "Pricing with markups in industries with increasing marginal costs," Documentos de Trabajo 256, Centro de Economía Aplicada, Universidad de Chile.
    11. Gaëtan Fournier & Marco Scarsini, 2014. "Hotelling Games on Networks: Efficiency of Equilibria," Documents de travail du Centre d'Economie de la Sorbonne 14033, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    12. Pieter Kleer, 2023. "Price of anarchy for parallel link networks with generalized mean objective," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 45(1), pages 27-55, March.
    13. Marco Scarsini & Tristan Tomala, 2012. "Repeated congestion games with bounded rationality," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(3), pages 651-669, August.
    14. Thanasis Lianeas & Evdokia Nikolova & Nicolas E. Stier-Moses, 2019. "Risk-Averse Selfish Routing," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 38-57, February.
    15. Cominetti, Roberto & Dose, Valerio & Scarsini, Marco, 2024. "Phase transitions of the price-of-anarchy function in multi-commodity routing games," Transportation Research Part B: Methodological, Elsevier, vol. 182(C).
    16. Knight, Vincent A. & Harper, Paul R., 2013. "Selfish routing in public services," European Journal of Operational Research, Elsevier, vol. 230(1), pages 122-132.
    17. Zijun Wu & Rolf H. Moehring & Chunying Ren & Dachuan Xu, 2020. "A convergence analysis of the price of anarchy in atomic congestion games," Papers 2007.14769, arXiv.org, revised Dec 2021.
    18. Chenlan Wang & Xuan Vinh Doan & Bo Chen, 2022. "Atomic congestion games with random players: network equilibrium and the price of anarchy," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 2123-2142, October.
    19. Harks, Tobias & Schröder, Marc & Vermeulen, Dries, 2019. "Toll caps in privatized road networks," European Journal of Operational Research, Elsevier, vol. 276(3), pages 947-956.
    20. Tamer Başar & Quanyan Zhu, 2011. "Prices of Anarchy, Information, and Cooperation in Differential Games," Dynamic Games and Applications, Springer, vol. 1(1), pages 50-73, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:mateco:v:86:y:2020:i:c:p:15-23. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jmateco .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.