IDEAS home Printed from https://ideas.repec.org/a/spr/joptap/v128y2006i2d10.1007_s10957-006-9021-z.html
   My bibliography  Save this article

Controlling the Cournot-Nash Chaos

Author

Listed:
  • A. Matsumoto

    (Chuo University)

Abstract

The recently developing theory of nonlinear dynamics shows that any economic model can generate a complex dynamics involving chaos if the nonlinearities become strong enough. This study constructs a nonlinear Cournot duopoly model, reveals conditions for the occurrence of chaos, and then considers how to control chaos. The main purpose of this paper is to demonstrate that chaos generated in Cournot competition is in a double bind from the long-run perspective: a firm with a lower marginal production cost prefers a stable (i.e., controlled) market to a chaotic (i.e., uncontrolled) market, while a firm with a higher marginal cost prefers the chaotic market.

Suggested Citation

  • A. Matsumoto, 2006. "Controlling the Cournot-Nash Chaos," Journal of Optimization Theory and Applications, Springer, vol. 128(2), pages 379-392, February.
    • Handle: RePEc:spr:joptap:v:128:y:2006:i:2:d:10.1007_s10957-006-9021-z
    DOI: 10.1007/s10957-006-9021-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10957-006-9021-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10957-006-9021-z?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. Huang, Weihong, 1995. "Caution implies profit," Journal of Economic Behavior & Organization, Elsevier, vol. 27(2), pages 257-277, July.
    2. Boldrin, Michele & Woodford, Michael, 1990. "Equilibrium models displaying endogenous fluctuations and chaos : A survey," Journal of Monetary Economics, Elsevier, vol. 25(2), pages 189-222, March.
    3. Bala, Venkatesh & Majumdar, Mukul & Mitra, Tapan, 1998. "A note on controlling a chaotic tatonnement," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 411-420, January.
    4. Michael Kopel, 1997. "Improving the performance of an economic system: Controlling chaos," Journal of Evolutionary Economics, Springer, vol. 7(3), pages 269-289.
    5. Dana, Rose-Anne & Montrucchio, Luigi, 1986. "Dynamic complexity in duopoly games," Journal of Economic Theory, Elsevier, vol. 40(1), pages 40-56, October.
    6. Rand, David, 1978. "Exotic phenomena in games and duopoly models," Journal of Mathematical Economics, Elsevier, vol. 5(2), pages 173-184, September.
    7. Day, Richard H, 1982. "Irregular Growth Cycles," American Economic Review, American Economic Association, vol. 72(3), pages 406-414, 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. 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.
    2. Wu, Ruijia & Van Gorder, Robert A., 2018. "Nonlinear dynamics of discrete time multi-level leader–follower games," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 240-250.
    3. Naimzada, A.K. & Raimondo, Roberto, 2018. "Heterogeneity and chaos in congestion games," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 278-291.
    4. Cavalli, Fausto & Naimzada, Ahmad, 2015. "Effect of price elasticity of demand in monopolies with gradient adjustment," Chaos, Solitons & Fractals, Elsevier, vol. 76(C), pages 47-55.
    5. Junhai Ma & Lijian Sun & Xueli Zhan, 2017. "Study on Triopoly Dynamic Game Model Based on Different Demand Forecast Methods in the Market," Complexity, Hindawi, vol. 2017, pages 1-12, July.
    6. Qiuxiang Li & Mengnan Shi & Yimin Huang, 2019. "A Dynamic Price Game Model in a Low-Carbon, Closed-Loop Supply Chain Considering Return Rates and Fairness Concern Behaviors," IJERPH, MDPI, vol. 16(11), pages 1-21, June.
    7. Tramontana, Fabio & Gardini, Laura & Puu, Tönu, 2010. "Global bifurcations in a piecewise-smooth Cournot duopoly game," Chaos, Solitons & Fractals, Elsevier, vol. 43(1), pages 15-24.
    8. Xin, Baogui & Peng, Wei & Kwon, Yekyung, 2020. "A discrete fractional-order Cournot duopoly game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 558(C).
    9. Baogui Xin & Wei Peng & Yekyung Kwon, 2019. "A fractional-order difference Cournot duopoly game with long memory," Papers 1903.04305, arXiv.org.

    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. Matsumoto, Akio & Nonaka, Yasuo, 2006. "Statistical dynamics in a chaotic Cournot model with complementary goods," Journal of Economic Behavior & Organization, Elsevier, vol. 61(4), pages 769-783, December.
    2. Alexeeva, Tatyana A. & Kuznetsov, Nikolay V. & Mokaev, Timur N., 2021. "Study of irregular dynamics in an economic model: attractor localization and Lyapunov exponents," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    3. Nijkamp, P. & Poot, J., 1991. "Lessons from non-linear dynamic economics," Serie Research Memoranda 0105, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    4. Luis A. Aguirre & Antonio Aguirre, 1997. "A tutorial introduction to nonlinear dynamics in economics," Nova Economia, Economics Department, Universidade Federal de Minas Gerais (Brazil), vol. 7(2), pages 9-47.
    5. Kopel, Michael & Westerhoff, Frank & Wieland, Cristian, 2008. "Regulating complex dynamics in firms and economic systems," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 911-919.
    6. Nijkamp, P. & Reggiani, A., 1990. "Spatio-temporal processes in dynamic logit models," Serie Research Memoranda 0063, VU University Amsterdam, Faculty of Economics, Business Administration and Econometrics.
    7. 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.
    8. Matsumoto, Akio, 2005. "Density function of piecewise linear transformation," Journal of Economic Behavior & Organization, Elsevier, vol. 56(4), pages 631-653, April.
    9. Antonio Linero-Bas & María Muñoz-Guillermo, 2021. "A Full Description of ω -Limit Sets of Cournot Maps Having Non-Empty Interior and Some Economic Applications," Mathematics, MDPI, vol. 9(4), pages 1-33, February.
    10. Bischi, Gian Italo & Naimzada, Ahmad K. & Sbragia, Lucia, 2007. "Oligopoly games with Local Monopolistic Approximation," Journal of Economic Behavior & Organization, Elsevier, vol. 62(3), pages 371-388, March.
    11. Gomes, Orlando, 2008. "Too much of a good thing: Endogenous business cycles generated by bounded technological progress," Economic Modelling, Elsevier, vol. 25(5), pages 933-945, September.
    12. Michele Boldrin, 1988. "Persistent Oscillations and Chaos in Dynamic Economic Models: Notes for a Survey," UCLA Economics Working Papers 458A, UCLA Department of Economics.
    13. Akhmet, Marat & Akhmetova, Zhanar & Fen, Mehmet Onur, 2014. "Chaos in economic models with exogenous shocks," Journal of Economic Behavior & Organization, Elsevier, vol. 106(C), pages 95-108.
    14. Tamotsu Onozaki, 2018. "Nonlinearity, Bounded Rationality, and Heterogeneity," Springer Books, Springer, number 978-4-431-54971-0, September.
    15. Cars H. Hommes & Marius I. Ochea & Jan Tuinstra, 2018. "Evolutionary Competition Between Adjustment Processes in Cournot Oligopoly: Instability and Complex Dynamics," Dynamic Games and Applications, Springer, vol. 8(4), pages 822-843, December.
    16. 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).
    17. Wieland, Cristian & Westerhoff, Frank H., 2005. "Exchange rate dynamics, central bank interventions and chaos control methods," Journal of Economic Behavior & Organization, Elsevier, vol. 58(1), pages 117-132, September.
    18. Tramontana, Fabio & Sushko, Iryna & Avrutin, Viktor, 2015. "Period adding structure in a 2D discontinuous model of economic growth," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 262-273.
    19. Ahmad K. Naimzada & Serena Sordi, 2018. "On controlling chaos in a discrete†time Walrasian tâtonnement process," Metroeconomica, Wiley Blackwell, vol. 69(1), pages 178-194, February.
    20. Frédéric Lordon, 1995. "Cycles et chaos dans un modèle hétérodoxe de croissance endogène," Revue Économique, Programme National Persée, vol. 46(6), pages 1405-1432.

    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:spr:joptap:v:128:y:2006:i:2:d:10.1007_s10957-006-9021-z. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.