IDEAS home Printed from https://ideas.repec.org/a/wsi/igtrxx/v08y2006i01ns0219198906000758.html
   My bibliography  Save this article

Global Bifurcations In Duopoly When The Cournot Point Is Destabilized Via A Subcritical Neimark Bifurcation

Author

Listed:
  • ANNA AGLIARI

    (Dip. Scienze Economiche e Sociali, Catholic University, Via Emilia Parmense, 84. Piacenza I-29100, Italy)

  • LAURA GARDINI

    (Dip. Scienze Economiche, University of Urbino "Carlo Bo", Urbino I-61029, Italy)

  • TONU PUU

    (Dep. Economics University of Umea, Umea SE-90187, Sweden)

Abstract

An adaptive oligopoly model, where the demand function is isoelastic and the competitors operate under constant marginal costs, is considered. The Cournot equilibrium point then loses stability through a subcritical Neimark bifurcation. The present paper focuses some global bifurcations, which precede the Neimark bifurcation, and produce other attractors which coexist with the still attractive Cournot fixed point.

Suggested Citation

  • Anna Agliari & Laura Gardini & Tonu Puu, 2006. "Global Bifurcations In Duopoly When The Cournot Point Is Destabilized Via A Subcritical Neimark Bifurcation," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 1-20.
    • Handle: RePEc:wsi:igtrxx:v:08:y:2006:i:01:n:s0219198906000758
    DOI: 10.1142/S0219198906000758
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219198906000758
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219198906000758?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.

    Citations

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


    Cited by:

    1. 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.
    2. Alina Szuz & Anna Agliari & Tonu Puu, 2015. "A Cournot triopoly with two identical producers," Gecomplexity Discussion Paper Series 13, Action IS1104 "The EU in the new complex geography of economic systems: models, tools and policy evaluation", revised Aug 2015.
    3. Luciano Fanti & Luca Gori & Cristiana Mammana & Elisabetta Michetti, 2018. "A model of growth with inherited tastes," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 163-186, November.
    4. S. S. Askar & A. Al-khedhairi, 2019. "Cournot Duopoly Games: Models and Investigations," Mathematics, MDPI, vol. 7(11), pages 1-15, November.
    5. Gori, Luca & Sodini, Mauro, 2017. "Price competition in a nonlinear differentiated duopoly," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 557-567.
    6. Fanti, Luciano & Gori, Luca, 2012. "The dynamics of a differentiated duopoly with quantity competition," Economic Modelling, Elsevier, vol. 29(2), pages 421-427.
    7. Agliari, Anna & Pecora, Nicolò & Szuz, Alina, 2022. "Appearance of closed invariant curves in a piecewise Cournot model with advertising," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    8. Gian Italo Bischi & Fabio Lamantia & Davide Radi, 2018. "Evolutionary oligopoly games with heterogeneous adaptive players," Chapters, in: Luis C. Corchón & Marco A. Marini (ed.), Handbook of Game Theory and Industrial Organization, Volume I, chapter 12, pages 343-370, Edward Elgar Publishing.
    9. Askar, S.S. & Al-khedhairi, A., 2020. "The dynamics of a business game: A 2D-piecewise smooth nonlinear map," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    10. Mikhail Anufriev & Davide Radi & Fabio Tramontana, 2018. "Some reflections on past and future of nonlinear dynamics in economics and finance," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 41(2), pages 91-118, November.
    11. Fabio Lamantia, 2011. "A Nonlinear Duopoly with Efficient Production-Capacity Levels," Computational Economics, Springer;Society for Computational Economics, vol. 38(3), pages 295-309, October.
    12. Tramontana, Fabio, 2010. "Heterogeneous duopoly with isoelastic demand function," Economic Modelling, Elsevier, vol. 27(1), pages 350-357, January.
    13. Bischi, Gian Italo & Cerboni Baiardi, Lorenzo, 2015. "A dynamic marketing model with best reply and inertia," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 145-156.
    14. 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.
    15. Domenico De Giovanni & Fabio Lamantia, 2017. "Evolutionary dynamics of a duopoly game with strategic delegation and isoelastic demand," Journal of Evolutionary Economics, Springer, vol. 27(5), pages 877-903, November.
    16. Bischi, Gian Italo & Lamantia, Fabio & Radi, Davide, 2015. "An evolutionary Cournot model with limited market knowledge," Journal of Economic Behavior & Organization, Elsevier, vol. 116(C), pages 219-238.
    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. Sameh Askar, 2021. "Complex Investigations of a Piecewise-Smooth Remanufacturing Bertrand Duopoly Game," Mathematics, MDPI, vol. 9(20), pages 1-13, October.
    19. Bischi Gian Italo & Lamantia Fabio, 2012. "Routes to Complexity Induced by Constraints in Cournot Oligopoly Games with Linear Reaction Functions," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 16(2), pages 1-30, April.
    20. Cerboni Baiardi, Lorenzo & Lamantia, Fabio & Radi, Davide, 2015. "Evolutionary competition between boundedly rational behavioral rules in oligopoly games," Chaos, Solitons & Fractals, Elsevier, vol. 79(C), pages 204-225.
    21. 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.

    More about this item

    Keywords

    Duopoly model; Subcritical Neimark bifurcation; Border collision bifurcation; Subject Classification: 37N40; Subject Classification: 70K; Subject Classification: 37G99;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

    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:wsi:igtrxx:v:08:y:2006:i:01:n:s0219198906000758. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/igtr/igtr.shtml .

    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.