IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2014y2014i1n970205.html

Complexity Analysis of a Master‐Slave Oligopoly Model and Chaos Control

Author

Listed:
  • Junhai Ma
  • Fang Zhang
  • Yanyan He

Abstract

We establish a master‐slave oligopoly game model with an upstream monopoly whose output is considered and two downstream oligopolies whose prices are considered. The existence and the local stable region of the Nash equilibrium point are investigated. The complex dynamic properties, such as bifurcation and chaos, are analyzed using bifurcation diagrams, the largest Lyapunov exponent diagrams, and the strange attractor graph. We further analyze the long‐run average profit of the three firms and find that they are all optimal in the stable region. In addition, delay feedback control method and limiter control method are used in nondelayed model to control chaos. Furthermore, a delayed master‐slave oligopoly game model is considered, and the three firms’ profit in various conditions is analyzed. We find that suitable delayed parameters are important for eliminating chaos and maximizing the profit of the players.

Suggested Citation

  • Junhai Ma & Fang Zhang & Yanyan He, 2014. "Complexity Analysis of a Master‐Slave Oligopoly Model and Chaos Control," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:970205
    DOI: 10.1155/2014/970205
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2014/970205
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2014/970205?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. Elsadany, A.A., 2012. "Competition analysis of a triopoly game with bounded rationality," Chaos, Solitons & Fractals, Elsevier, vol. 45(11), pages 1343-1348.
    2. Fanti, Luciano & Gori, Luca, 2012. "The dynamics of a differentiated duopoly with quantity competition," Economic Modelling, Elsevier, vol. 29(2), pages 421-427.
    3. Agiza, H.N. & Hegazi, A.S. & Elsadany, A.A., 2002. "Complex dynamics and synchronization of a duopoly game with bounded rationality," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 58(2), pages 133-146.
    4. 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.
    5. Du, Jian-guo & Fan, Yue-qian & Sheng, Zhao-han & Hou, Yun-zhang, 2013. "Dynamics analysis and chaos control of a duopoly game with heterogeneous players and output limiter," Economic Modelling, Elsevier, vol. 33(C), pages 507-516.
    6. 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.
    7. 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)

    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. Joaquín Andaluz & Gloria Jarne, 2019. "On price stability and the nature of product differentiation," Journal of Evolutionary Economics, Springer, vol. 29(2), pages 741-762, April.
    2. Sameh Askar & Abdulaziz Foul & Tarek Mahrous & Saleh Djemele & Emad Ibrahim, 2021. "Global and Local Analysis for a Cournot Duopoly Game with Two Different Objective Functions," Mathematics, MDPI, vol. 9(23), pages 1-14, December.
    3. 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.
    4. Du, Jian-guo & Fan, Yue-qian & Sheng, Zhao-han & Hou, Yun-zhang, 2013. "Dynamics analysis and chaos control of a duopoly game with heterogeneous players and output limiter," Economic Modelling, Elsevier, vol. 33(C), pages 507-516.
    5. Askar, S.S., 2021. "On complex dynamics of Cournot-Bertrand game with asymmetric market information," Applied Mathematics and Computation, Elsevier, vol. 393(C).
    6. Zhang, Ming & Wang, Guanghui & Xu, Jin & Qu, Cunquan, 2020. "Dynamic contest model with bounded rationality," Applied Mathematics and Computation, Elsevier, vol. 370(C).
    7. Peng, Yu & Lu, Qian & Xiao, Yue, 2016. "A dynamic Stackelberg duopoly model with different strategies," Chaos, Solitons & Fractals, Elsevier, vol. 85(C), pages 128-134.
    8. Askar, S.S., 2022. "Nonlinear dynamic investigations and global analysis of a Cournot duopoly game with two different objectives," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    9. 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.
    10. S. S. Askar, 2022. "On the Dynamics of Cournot Duopoly Game with Governmental Taxes," Complexity, John Wiley & Sons, vol. 2022(1).
    11. Kosmas Papadopoulos & Georges Sarafopoulos & Evangelos Ioannidis, 2025. "Delayed Feedback Chaos Control on a Cournot Game with Relative Profit Maximization," Mathematics, MDPI, vol. 13(15), pages 1-18, July.
    12. 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.
    13. 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.
    14. 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).
    15. Fausto Cavalli & Ahmad Naimzada & Marina Pireddu, 2015. "Effects of Size, Composition, and Evolutionary Pressure in Heterogeneous Cournot Oligopolies with Best Response Decisional Mechanisms," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-17, May.
    16. Elsadany, A.A., 2017. "Dynamics of a Cournot duopoly game with bounded rationality based on relative profit maximization," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 253-263.
    17. PAPADOPOULOS Kosmas & SARAFOPOULOS Georges, 2019. "Dynamics of a Cournot Game with Differentiated Goods and Asymmetric Cost Functions based on Relative Profit Maximization," European Journal of Interdisciplinary Studies, Bucharest Economic Academy, issue 02, June.
    18. Fanti, Luciano & Gori, Luca, 2011. "Cross-ownership and stability in a Cournot duopoly," MPRA Paper 34574, University Library of Munich, Germany.
    19. A. A. Elsadany & A. M. Awad, 2016. "Dynamical analysis and chaos control in a heterogeneous Kopel duopoly game," Indian Journal of Pure and Applied Mathematics, Springer, vol. 47(4), pages 617-639, December.
    20. Junhai Ma & Weiya Di & Hao Ren, 2017. "Complexity Dynamic Character Analysis of Retailers Based on the Share of Stochastic Demand and Service," Complexity, Hindawi, vol. 2017, pages 1-12, 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:2014:y:2014:i:1:n:970205. 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.