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Oligopoly model with recurrent renewal of capital revisited

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  • Panchuk, A.
  • Puu, T.

Abstract

The aim of the present paper is to investigate an oligopoly market, modelled by using CES production function in combination with the isoelastic demand function. It is supposed that the competitors act not under constant, but eventually decaying returns, and thus, from time to time they need to renew their capital equipment, choosing its optimal amount according to the current market situation. It is shown that the asymptotic trajectories depend essentially on the value of the global capital durability, and are also sensitive to the initial choice of individual inactivity times. In particular, the firms may merge into different groups renewing their capitals simultaneously, which lead to distinct dynamical patterns. It is also studied how the capital wearing out rate influences the system behaviour.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:108:y:2015:i:c:p:119-128
    DOI: 10.1016/j.matcom.2013.09.007
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    References listed on IDEAS

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    1. 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.
    2. Agliari, Anna, 2006. "Homoclinic connections and subcritical Neimark bifurcation in a duopoly model with adaptively adjusted productions," Chaos, Solitons & Fractals, Elsevier, vol. 29(3), pages 739-755.
    3. Puu, T. & Panchuk, A., 2009. "Oligopoly and stability," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2505-2516.
    4. Bischi, Gian-Italo & Stefanini, Luciano & Gardini, Laura, 1998. "Synchronization, intermittency and critical curves in a duopoly game," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 44(6), pages 559-585.
    5. M. Kopel & F. Szidarovszky, 2006. "Resource Dynamics under Partial Cooperation in an Oligopoly," Journal of Optimization Theory and Applications, Springer, vol. 128(2), pages 393-410, February.
    6. Angelini, Natascia & Dieci, Roberto & Nardini, Franco, 2009. "Bifurcation analysis of a dynamic duopoly model with heterogeneous costs and behavioural rules," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(10), pages 3179-3196.
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    Cited by:

    1. 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.
    2. Li, Bo & Liang, Houjun & Shi, Lian & He, Qizhi, 2022. "Complex dynamics of Kopel model with nonsymmetric response between oligopolists," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    3. 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.

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