IDEAS home Printed from https://ideas.repec.org/a/wly/jnddns/v2016y2016i1n7342405.html

Analysis and Control of the Complex Dynamics of a Multimarket Cournot Investment Game with Bounded Rationality

Author

Listed:
  • LiuWei Zhao

Abstract

A dynamic multimarket Cournot model is introduced based on a specific inverse demand function. Puu’s incomplete information approach, as a realistic method, is used to contract the corresponding dynamical model under this function. Therefore, some stability analysis is carried out on the model to detect the stability and instability conditions of the system’s Nash equilibrium. Based on the analysis, some dynamic phenomena such as bifurcation and chaos are found. Numerical simulations are used to provide experimental evidence for the complicated behaviors of the system evolution. It is observed that the equilibrium of the system can lose stability via flip bifurcation or Neimark‐Sacker bifurcation and time‐delayed feedback control is used to stabilize the chaotic behaviors of the system.

Suggested Citation

  • LiuWei Zhao, 2016. "Analysis and Control of the Complex Dynamics of a Multimarket Cournot Investment Game with Bounded Rationality," Discrete Dynamics in Nature and Society, John Wiley & Sons, vol. 2016(1).
    • Handle: RePEc:wly:jnddns:v:2016:y:2016:i:1:n:7342405
    DOI: 10.1155/2016/7342405
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2016/7342405
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2016/7342405?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
    ---><---

    References listed on IDEAS

    as
    1. Subhadip Chakrabarti & Hans Haller, 2011. "An Analysis Of Advertising Wars," Manchester School, University of Manchester, vol. 79(1), pages 100-124, January.
    2. Avinash Dixit, 1979. "A Model of Duopoly Suggesting a Theory of Entry Barriers," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 20-32, Spring.
    3. Ding, Zhanwen & Wang, Qiao & Jiang, Shumin, 2014. "Analysis on the dynamics of a Cournot investment game with bounded rationality," Economic Modelling, Elsevier, vol. 39(C), pages 204-212.
    4. Puu, T., 1998. "The chaotic duopolists revisited," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 385-394, January.
    5. Billand, Pascal & Bravard, Christophe & Chakrabarti, Subhadip & Sarangi, Sudipta, 2010. "Networks of Collaboration in Multi-market Oligopolies," MPRA Paper 28188, University Library of Munich, Germany.
    6. R. D. Theocharis, 1960. "On the Stability of the Cournot Solution on the Oligopoly Problem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 27(2), pages 133-134.
    7. Zhang, Jixiang & Da, Qingli & Wang, Yanhua, 2007. "Analysis of nonlinear duopoly game with heterogeneous players," Economic Modelling, Elsevier, vol. 24(1), pages 138-148, January.
    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. 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.
    2. Ding, Zhanwen & Li, Qiang & Jiang, Shumin & Wang, Xuedi, 2015. "Dynamics in a Cournot investment game with heterogeneous players," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 939-950.
    3. Zhao, LiuWei & Du, Jianguo & Wang, QiWei, 2019. "Nonlinear analysis and chaos control of the complex dynamics of multi-market Cournot game with bounded rationality," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 162(C), pages 45-57.
    4. 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.
    5. 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.
    6. Kamalinejad, Howra & Majd, Vahid Johari & Kebriaei, Hamed & Rahimi-Kian, Ashkan, 2010. "Cournot games with linear regression expectations in oligopolistic markets," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(9), pages 1874-1885.
    7. Shi, Lian & Sheng, Zhaohan & Xu, Feng, 2015. "The dynamics of competition in remanufacturing: A stability analysis," Economic Modelling, Elsevier, vol. 50(C), pages 245-253.
    8. Georges SARAFOPOULOS & Kosmas PAPADOPOULOS, 2017. "On A Cournot Duopoly Game With Differentiated Goods, Heterogeneous Expectations And A Cost Function Including Emission Costs," Scientific Bulletin - Economic Sciences, University of Pitesti, vol. 16(1), pages 11-22.
    9. Ding, Zhanwen & Wang, Qiao & Jiang, Shumin, 2014. "Analysis on the dynamics of a Cournot investment game with bounded rationality," Economic Modelling, Elsevier, vol. 39(C), pages 204-212.
    10. Zhengyang Liu & Haolin Lu & Liang Shan & Zihe Wang, 2024. "On the Oscillations in Cournot Games with Best Response Strategies," Papers 2410.09435, arXiv.org, revised May 2025.
    11. Fanti, Luciano & Gori, Luca, 2012. "The dynamics of a differentiated duopoly with quantity competition," Economic Modelling, Elsevier, vol. 29(2), pages 421-427.
    12. S. S. Askar & Mona F. EL-Wakeel & M. A. Alrodaini, 2018. "Exploration of Complex Dynamics for Cournot Oligopoly Game with Differentiated Products," Complexity, Hindawi, vol. 2018, pages 1-13, February.
    13. Luciano Fanti & Luca Gori, 2011. "Stability in a Cournot duopoly under asymmetric unionism," Discussion Papers 2011/123, Dipartimento di Economia e Management (DEM), University of Pisa, Pisa, Italy.
    14. Peng, Yu & Lu, Qian, 2015. "Complex dynamics analysis for a duopoly Stackelberg game model with bounded rationality," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 259-268.
    15. Joaquín Andaluz & Gloria Jarne, 2016. "Stability of vertically differentiated Cournot and Bertrand-type models when firms are boundedly rational," Annals of Operations Research, Springer, vol. 238(1), pages 1-25, March.
    16. Yu, Weisheng & Yu, Yu, 2014. "A dynamic duopoly model with bounded rationality based on constant conjectural variation," Economic Modelling, Elsevier, vol. 37(C), pages 103-112.
    17. Ahmed, E. & Elettreby, M.F., 2014. "Controls of the complex dynamics of a multi-market Cournot model," Economic Modelling, Elsevier, vol. 37(C), pages 251-254.
    18. Frederik Schmidt, 2008. "The Stability of Dynamic Contests with Asymmetric and Endogenous Prizes," Economics Bulletin, AccessEcon, vol. 3(4), pages 1-9.
    19. Fabio Lamantia & Anghel Negriu & Jan Tuinstra, 2018. "Technology choice in an evolutionary oligopoly game," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 335-356, November.
    20. Zhang, Ming & Wang, Guanghui & Xu, Jin & Qu, Cunquan, 2020. "Dynamic contest model with bounded rationality," Applied Mathematics and Computation, Elsevier, vol. 370(C).

    More about this item

    Statistics

    Access and download statistics

    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:wly:jnddns:v:2016:y:2016:i:1:n:7342405. 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: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/3059 .

    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.