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The dynamics of a triopoly Cournot game when the competitors operate under capacity constraints

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  • Puu, Tönu
  • Marín, Manuel Ruíz

Abstract

This article considers Cournot oligopoly with three competitors, given an iso-elastic demand function, and cost functions that asymptotically go to infinity when capacity limits are approached. It is shown that for some parameter values (capacity limits) the Cournot equilibrium point loses stability through a Neimark-Sacker bifurcation. In addition global bifurcation scenarios are simulated numerically, and some are illustrated through Arnol’d tongues in the parameter plane.

Suggested Citation

  • Puu, Tönu & Marín, Manuel Ruíz, 2006. "The dynamics of a triopoly Cournot game when the competitors operate under capacity constraints," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 403-413.
    • Handle: RePEc:eee:chsofr:v:28:y:2006:i:2:p:403-413
    DOI: 10.1016/j.chaos.2005.05.034
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    References listed on IDEAS

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    1. Rand, David, 1978. "Exotic phenomena in games and duopoly models," Journal of Mathematical Economics, Elsevier, vol. 5(2), pages 173-184, September.
    2. Agliari, Anna & Gardini, Laura & Puu, Tönu, 2005. "Some global bifurcations related to the appearance of closed invariant curves," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 68(3), pages 201-219.
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    Cited by:

    1. Xin, Baogui & Ma, Junhai & Gao, Qin, 2009. "The complexity of an investment competition dynamical model with imperfect information in a security market," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2425-2438.
    2. 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.
    3. Jose S. Cánovas & Anastasiia Panchuk & Tonu Puu, 2015. "Role of reinvestment in a competitive market," Gecomplexity Discussion Paper Series 12, Action IS1104 "The EU in the new complex geography of economic systems: models, tools and policy evaluation", revised Apr 2015.
    4. Halkos, George & Papageorgiou, George, 2012. "Simple taxation schemes on non–renewable resources extraction," MPRA Paper 40945, University Library of Munich, Germany.
    5. Cánovas, Jose S. & Panchuk, Anastasiia & Puu, Tönu, 2015. "Asymptotic dynamics of a piecewise smooth map modelling a competitive market," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 117(C), pages 20-38.
    6. Puu, Tonu & Tramontana, Fabio, 2019. "Can Bertrand and Cournot oligopolies be combined?," Chaos, Solitons & Fractals, Elsevier, vol. 125(C), pages 97-107.
    7. Andrikopoulos, A. & Dassiou, X., 2018. "Exchange-rate exposure in a “Rule of Three” Model," Working Papers 18/02, Department of Economics, City University London.
    8. Panchuk, A. & Puu, T., 2015. "Oligopoly model with recurrent renewal of capital revisited," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 108(C), pages 119-128.
    9. Ting Li & Dongyun Yan & Xiaogang Ma, 2019. "Stability Analysis and Chaos Control of Recycling Price Game Model for Manufacturers and Retailers," Complexity, Hindawi, vol. 2019, pages 1-13, July.

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