[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v320y2003icp512-524.html
   My bibliography  Save this article

Nonlinear dynamics in the Cournot duopoly game with heterogeneous players

Author

Listed:
  • Agiza, H.N.
  • Elsadany, A.A.
Abstract
We analyze a nonlinear discrete-time Cournot duopoly game, where players have heterogeneous expectations. Two types of players are considered: boundedly rational and naive expectations. In this study we show that the dynamics of the duopoly game with players whose beliefs are heterogeneous, may become complicated. The model gives more complex chaotic and unpredictable trajectories as a consequence of increasing the speed of adjustment of boundedly rational player. The equilibrium points and local stability of the duopoly game are investigated. As some parameters of the model are varied, the stability of the Nash equilibrium point is lost and the complex (periodic or chaotic) behavior occurs. Numerical simulations are presented to show that players with heterogeneous beliefs make the duopoly game behave chaotically. Also, we get the fractal dimension of the chaotic attractor of our map which is equivalent to the dimension of Henon map.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:320:y:2003:i:c:p:512-524
    DOI: 10.1016/S0378-4371(02)01648-5
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437102016485
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/S0378-4371(02)01648-5?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. Den Haan, Wouter J., 2001. "The importance of the number of different agents in a heterogeneous asset-pricing model," Journal of Economic Dynamics and Control, Elsevier, vol. 25(5), pages 721-746, May.
    2. Puu, T., 1998. "The chaotic duopolists revisited," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 385-394, January.
    3. Bischi, Gian Italo & Kopel, Michael, 2001. "Equilibrium selection in a nonlinear duopoly game with adaptive expectations," Journal of Economic Behavior & Organization, Elsevier, vol. 46(1), pages 73-100, September.
    4. 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.
    5. Nabih Agiza, Hamdy & Italo Bischi, Gian & Kopel, Michael, 1999. "Multistability in a dynamic Cournot game with three oligopolists," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 51(1), pages 63-90.
    6. 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.
    7. Brock, William A. & Hommes, Cars H., 1998. "Heterogeneous beliefs and routes to chaos in a simple asset pricing model," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1235-1274, August.
    8. Rand, David, 1978. "Exotic phenomena in games and duopoly models," Journal of Mathematical Economics, Elsevier, vol. 5(2), pages 173-184, September.
    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. Tomasz Dubiel-Teleszyński, 2010. "Complex Dynamics in a Bertrand Duopoly Game with Heterogeneous Players," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 2(2), pages 95-116, March.
    2. Troy Tassier, 2013. "Handbook of Research on Complexity, by J. Barkley Rosser, Jr. and Edward Elgar," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 39(1), pages 132-133.
    3. Antonio Doria, Francisco, 2011. "J.B. Rosser Jr. , Handbook of Research on Complexity, Edward Elgar, Cheltenham, UK--Northampton, MA, USA (2009) 436 + viii pp., index, ISBN 978 1 84542 089 5 (cased)," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1-2), pages 196-204, April.
    4. 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.
    5. 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.
    6. 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.
    7. Kebriaei, Hamed & Rahimi-Kian, Ashkan, 2011. "Decision making in dynamic stochastic Cournot games," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(6), pages 1202-1217.
    8. 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.
    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. 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.
    11. Tramontana, Fabio, 2010. "Heterogeneous duopoly with isoelastic demand function," Economic Modelling, Elsevier, vol. 27(1), pages 350-357, January.
    12. Zhaohan Sheng & Jianguo Du & Qiang Mei & Tingwen Huang, 2013. "New Analyses of Duopoly Game with Output Lower Limiters," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-10, February.
    13. Villena, Marcelo J. & Araneda, Axel A., 2017. "Dynamics and stability in retail competition," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 134(C), pages 37-53.
    14. Xin, Baogui & Chen, Tong, 2011. "On a master-slave Bertrand game model," Economic Modelling, Elsevier, vol. 28(4), pages 1864-1870, July.
    15. Fanti, Luciano & Gori, Luca, 2012. "The dynamics of a differentiated duopoly with quantity competition," Economic Modelling, Elsevier, vol. 29(2), pages 421-427.
    16. Tamotsu Onozaki, 2018. "Nonlinearity, Bounded Rationality, and Heterogeneity," Springer Books, Springer, number 978-4-431-54971-0, December.
    17. Fanti, Luciano & Gori, Luca, 2012. "The codetermined firm in a Cournot duopoly: A stability analysis," Economic Modelling, Elsevier, vol. 29(4), pages 1242-1247.
    18. 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.
    19. Ueda, Masahiko, 2019. "Effect of information asymmetry in Cournot duopoly game with bounded rationality," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.
    20. Bacchiocchi, Andrea & Bischi, Gian Italo & Giombini, Germana, 2022. "Non-performing loans, expectations and banking stability: A dynamic model," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).

    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:phsmap:v:320:y:2003:i:c:p:512-524. 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.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.