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Controlling the Cournot-Nash Chaos

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  • 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
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    References listed on IDEAS

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    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.

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