IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2013y2013i1n251702.html

Complex Dynamics Analysis for a Cournot‐Bertrand Mixed Game Model with Delayed Bounded Rationality

Author

Listed:
  • Junhai Ma
  • Hongwu Wang

Abstract

A Cournot‐Bertrand mixed duopoly game model is constructed. The existence and local stable region of the Nash equilibria point are investigated. Complex dynamic properties such as bifurcation and route to chaos are analyzed using parameter basin plots. The strange attractors are also studied when the system is in chaotic states. Furthermore, considering the memory of the market, a delayed Cournot‐Bertrand mixed model is considered and the results show that the delayed system has the same Nash equilibrium and has a higher chance of reaching steady states or cycles than the model without delay. So making full use of the historical data can improve the system’s stability.

Suggested Citation

  • Junhai Ma & Hongwu Wang, 2013. "Complex Dynamics Analysis for a Cournot‐Bertrand Mixed Game Model with Delayed Bounded Rationality," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:251702
    DOI: 10.1155/2013/251702
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2013/251702
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2013/251702?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. Naimzada, A.K. & Tramontana, F., 2012. "Dynamic properties of a Cournot–Bertrand duopoly game with differentiated products," Economic Modelling, Elsevier, vol. 29(4), pages 1436-1439.
    2. Piercarlo Zanchettin, 2006. "Differentiated Duopoly with Asymmetric Costs," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 15(4), pages 999-1015, December.
    3. Cees Diks & Cars Hommes & Valentyn Panchenko & Roy Weide, 2008. "E&F Chaos: A User Friendly Software Package for Nonlinear Economic Dynamics," Computational Economics, Springer;Society for Computational Economics, vol. 32(1), pages 221-244, September.
    4. Steven D. Sklivas, 1987. "The Strategic Choice of Managerial Incentives," RAND Journal of Economics, The RAND Corporation, vol. 18(3), pages 452-458, Autumn.
    5. Tremblay, Carol Horton & Tremblay, Victor J., 2011. "The Cournot-Bertrand model and the degree of product differentiation," Economics Letters, Elsevier, vol. 111(3), pages 233-235, June.
    6. Hackner, Jonas, 2000. "A Note on Price and Quantity Competition in Differentiated Oligopolies," Journal of Economic Theory, Elsevier, vol. 93(2), pages 233-239, August.
    7. Vives, Xavier, 1985. "On the efficiency of Bertrand and Cournot equilibria with product differentation," Journal of Economic Theory, Elsevier, vol. 36(1), pages 166-175, June.
    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. Ahmed, Rizwan & Qureshi, M. Zubair Akbar & Abbas, Muhammad & Mumtaz, Nida, 2025. "Bifurcation and chaos control in a heterogeneous Cournot-Bertrand duopoly game model," Chaos, Solitons & Fractals, Elsevier, vol. 190(C).
    2. Junhai Ma & Yuehong Guo, 2014. "Research on Third‐Party Collecting Game Model with Competition in Closed‐Loop Supply Chain Based on Complex Systems Theory," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

    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. Hsiao-Chi Chen & Yunshyong Chow & Shi-Miin Liu, 2024. "Dynamics of Cournot and Bertrand Firms: Exploring Imitation and Replicator Processes," Dynamic Games and Applications, Springer, vol. 14(5), pages 1057-1092, November.
    2. S. Askar, 2014. "On Cournot–Bertrand competition with differentiated products," Annals of Operations Research, Springer, vol. 223(1), pages 81-93, December.
    3. 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.
    4. Manasakis, Constantine & Vlassis, Minas, 2014. "Downstream mode of competition with upstream market power," Research in Economics, Elsevier, vol. 68(1), pages 84-93.
    5. Luciano Fanti & Nicola Meccheri, 2015. "On the Cournot–Bertrand Profit Differential and the Structure of Unionisation in a Managerial Duopoly," Australian Economic Papers, Wiley Blackwell, vol. 54(4), pages 266-287, December.
    6. S. S. Askar, 2022. "On the Dynamics of Cournot Duopoly Game with Governmental Taxes," Complexity, John Wiley & Sons, vol. 2022(1).
    7. Bian, Junsong & Lai, Kin Keung & Hua, Zhongsheng & Zhao, Xuan & Zhou, Guanghui, 2018. "Bertrand vs. Cournot competition in distribution channels with upstream collusion," International Journal of Production Economics, Elsevier, vol. 204(C), pages 278-289.
    8. Ryo Sakamoto & Kyle Stiegert, 2018. "Comparing competitive toughness to benchmark outcomes in retail oligopoly pricing," Agribusiness, John Wiley & Sons, Ltd., vol. 34(1), pages 44-60, December.
    9. Delbono, Flavio & Lambertini, Luca, 2016. "Ranking Bertrand, Cournot and supply function equilibria in oligopoly," Energy Economics, Elsevier, vol. 60(C), pages 73-78.
    10. Eleni Dalla, 2025. "Regulatory Impacts on Banking Behavior & Financial Stability: Insights from a Mixed-Oligopoly Model," International Advances in Economic Research, Springer;International Atlantic Economic Society, vol. 31(3), pages 125-137, August.
    11. Fanti, Luciano & Gori, Luca & Mammana, Cristiana & Michetti, Elisabetta, 2014. "Local and global dynamics in a duopoly with price competition and market share delegation," Chaos, Solitons & Fractals, Elsevier, vol. 69(C), pages 253-270.
    12. Olga Rozanova, 2017. "The possibility to renegotiate the contracts and the equilibrium mode of competition in vertically related markets," Economics Bulletin, AccessEcon, vol. 37(3), pages 1573-1580.
    13. Silveira, Douglas & Vasconcelos, Silvinha, 2020. "Essays on duopoly competition with asymmetric firms: Is profit maximization always an evolutionary stable strategy?," International Journal of Production Economics, Elsevier, vol. 225(C).
    14. Manipushpak Mitra & Rupayan Pal & Arindam Paul & P. M. Sharada, 2020. "Equilibrium Coexistence of Public and Private Firms and the Plausibility of Price Competition," Journal of Institutional and Theoretical Economics (JITE), Mohr Siebeck, Tübingen, vol. 176(2), pages 217-242.
    15. Ray-Yun Chang & Yan-Shu Lin & Jin-Li Hu, 2015. "Mixed Competition and Patent Licensing," Australian Economic Papers, Wiley Blackwell, vol. 54(4), pages 229-249, December.
    16. 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.
    17. Dermot Leahy & J. Peter Neary, 2021. "When the threat is stronger than the execution: trade and welfare under oligopoly," RAND Journal of Economics, RAND Corporation, vol. 52(3), pages 471-495, September.
    18. Shih‐Shen Chen & Chu‐Chuan Hsu & Po‐Sheng Ko, 2025. "Asymmetric Choice of Relative‐Performance Delegation Under Duopoly Competition With Vertical Product‐Quality Difference," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 46(5), pages 2869-2875, July.
    19. Askar, S.S., 2021. "On complex dynamics of Cournot-Bertrand game with asymmetric market information," Applied Mathematics and Computation, Elsevier, vol. 393(C).
    20. Hsiao‐Chi Chen & Shi‐Miin Liu & Sung‐Chi Lin, 2023. "Spatial agglomeration or dispersion under Cournot‐Bertrand competition," Manchester School, University of Manchester, vol. 91(5), pages 414-438, September.

    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:jnlaaa:v:2013:y:2013:i:1:n:251702. 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/4058 .

    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.