IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v321y2018icp333-348.html
   My bibliography  Save this article

Chaotic congestion games

Author

Listed:
  • Naimzada, Ahmad Kabir
  • Raimondo, Roberto

Abstract

We analyze a class of congestion games where two agents must send a finite amount of goods from an initial location to a terminal one. To do so the agents must use resources which are costly and costs are load dependent. In this context we assume that the agents have limited computational capability and they use a gradient rule as a decision mechanism. By introducing an appropriate dynamical system, which has the steady state exactly at the unique Nash equilibrium of the static congestion game, we investigate the dynamical behavior of the game. We provide a local stability condition in terms of the agents’ reactivity and the nonlinearity of the cost functions. In particular we show numerically that there is a route to complex dynamics: a cascade of flip-bifurcation leading to periodic cycles and finally to chaos.

Suggested Citation

  • Naimzada, Ahmad Kabir & Raimondo, Roberto, 2018. "Chaotic congestion games," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 333-348.
    • Handle: RePEc:eee:apmaco:v:321:y:2018:i:c:p:333-348
    DOI: 10.1016/j.amc.2017.10.021
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300317307208
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2017.10.021?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. Agiza, H.N. & Elsadany, A.A., 2003. "Nonlinear dynamics in the Cournot duopoly game with heterogeneous players," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 320(C), pages 512-524.
    2. G.‐I. Bischi & M. Gallegati & A. Naimzada, 1999. "Symmetry‐breaking bifurcations and representativefirm in dynamic duopoly games," Annals of Operations Research, Springer, vol. 89(0), pages 252-271, January.
    3. 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.
    4. 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.
    5. Selten, R. & Chmura, T. & Pitz, T. & Kube, S. & Schreckenberg, M., 2007. "Commuters route choice behaviour," Games and Economic Behavior, Elsevier, vol. 58(2), pages 394-406, February.
    6. Tramontana, Fabio, 2010. "Heterogeneous duopoly with isoelastic demand function," Economic Modelling, Elsevier, vol. 27(1), pages 350-357, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Yu, Yu & Yu, Weisheng, 2021. "The stability and duality of dynamic Cournot and Bertrand duopoly model with comprehensive preference," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    2. Askar, S.S., 2021. "On complex dynamics of Cournot-Bertrand game with asymmetric market information," Applied Mathematics and Computation, Elsevier, vol. 393(C).
    3. S. S. Askar & A. Al-khedhairi, 2019. "Analysis of a Four-Firm Competition Based on a Generalized Bounded Rationality and Different Mechanisms," Complexity, Hindawi, vol. 2019, pages 1-12, May.
    4. Askar, S.S., 2022. "On the dynamics of Cournot duopoly game with private firms: Investigations and analysis," Applied Mathematics and Computation, Elsevier, vol. 432(C).
    5. Sameh S. Askar, 2020. "The Influences of Asymmetric Market Information on the Dynamics of Duopoly Game," Mathematics, MDPI, vol. 8(7), pages 1-12, July.
    6. Sameh S. Askar, 2020. "A Dynamic Duopoly Model: When a Firm Shares the Market with Certain Profit," Mathematics, MDPI, vol. 8(10), pages 1-13, October.
    7. Naimzada, A.K. & Raimondo, Roberto, 2018. "Heterogeneity and chaos in congestion games," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 278-291.

    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. Naimzada, A.K. & Raimondo, Roberto, 2018. "Heterogeneity and chaos in congestion games," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 278-291.
    2. Luciano Fanti & Luca Gori, 2013. "Stability Analysis in a Bertrand Duopoly with Different Product Quality and Heterogeneous Expectations," Journal of Industry, Competition and Trade, Springer, vol. 13(4), pages 481-501, December.
    3. Fanti, Luciano & Gori, Luca & Sodini, Mauro, 2012. "Nonlinear dynamics in a Cournot duopoly with relative profit delegation," Chaos, Solitons & Fractals, Elsevier, vol. 45(12), pages 1469-1478.
    4. Fanti, Luciano & Gori, Luca, 2011. "The dynamics of a Bertrand duopoly with differentiated products and bounded rational firms revisited," MPRA Paper 33268, University Library of Munich, Germany.
    5. Cerboni Baiardi, Lorenzo & Naimzada, Ahmad K., 2019. "An oligopoly model with rational and imitation rules," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 156(C), pages 254-278.
    6. Lorenzo Cerboni Baiardi & Ahmad K. Naimzada, 2018. "An evolutionary model with best response and imitative rules," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 313-333, November.
    7. Sameh S Askar & Abdulrahman Al-Khedhairi, 2020. "Local and Global Dynamics of a Constraint Profit Maximization for Bischi–Naimzada Competition Duopoly Game," Mathematics, MDPI, vol. 8(9), pages 1-16, August.
    8. Lorenzo Cerboni Baiardi & Ahmad K. Naimzada, 2019. "An evolutionary Cournot oligopoly model with imitators and perfect foresight best responders," Metroeconomica, Wiley Blackwell, vol. 70(3), pages 458-475, July.
    9. Cerboni Baiardi, Lorenzo & Naimzada, Ahmad K., 2018. "An oligopoly model with best response and imitation rules," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 193-205.
    10. Zhang, Ming & Wang, Guanghui & Xu, Jin & Qu, Cunquan, 2020. "Dynamic contest model with bounded rationality," Applied Mathematics and Computation, Elsevier, vol. 370(C).
    11. Cavalli, Fausto & Naimzada, Ahmad & Pireddu, Marina, 2015. "Heterogeneity and the (de)stabilizing role of rationality," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 226-244.
    12. Fanti, Luciano & Gori, Luca, 2013. "Efficient bargaining versus right to manage: A stability analysis in a Cournot duopoly with trade unions," Economic Modelling, Elsevier, vol. 30(C), pages 205-211.
    13. Raimondo, Roberto, 2020. "Pathwise smooth splittable congestion games and inefficiency," Journal of Mathematical Economics, Elsevier, vol. 86(C), pages 15-23.
    14. Andaluz, J. & Elsadany, A.A. & Jarne, G., 2017. "Nonlinear Cournot and Bertrand-type dynamic triopoly with differentiated products and heterogeneous expectations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 132(C), pages 86-99.
    15. Xin, Baogui & Chen, Tong, 2011. "On a master-slave Bertrand game model," Economic Modelling, Elsevier, vol. 28(4), pages 1864-1870, July.
    16. Fanti, Luciano & Gori, Luca, 2012. "The dynamics of a differentiated duopoly with quantity competition," Economic Modelling, Elsevier, vol. 29(2), pages 421-427.
    17. Sameh S. Askar, 2020. "A Dynamic Duopoly Model: When a Firm Shares the Market with Certain Profit," Mathematics, MDPI, vol. 8(10), pages 1-13, October.
    18. Luciano Fanti, 2015. "Environmental Standards and Cournot Duopoly: A Stability Analysis," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 61(4), pages 577-593, August.
    19. Fanti, Luciano & Gori, Luca & Sodini, Mauro, 2015. "Nonlinear dynamics in a Cournot duopoly with isoelastic demand," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 108(C), pages 129-143.
    20. Fanti, Luciano & Gori, Luca, 2011. "Stability analysis in a Cournot duopoly with managerial sales delegation and bounded rationality," MPRA Paper 33828, University Library of Munich, Germany.

    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:apmaco:v:321:y:2018:i:c:p:333-348. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.