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Role of reinvestment in a competitive market

Author

Listed:
  • Jose S. Cánovas

    (Universidad Polit Ì ecnica de Cartagena, Departamento de Matematica Aplicada y Estad Ì Ä±stica)

  • Anastasiia Panchuk

    (nstitute of Mathematics, National Academy of Sciences of Ukraine)

  • Tonu Puu

    (CERUM, Umea University, SE-90187 Umea, Sweden)

Abstract

In the present work we study asymptotic dynamics of a multi-dimensional piecewise smooth map which models an oligopoly market where competitors use adaptive scheme for reaction choice. Each competitor also defines the moment for renewing the capital equipment depending on how intensively the latter is used. Namely, the larger output is produced, the quicker the capital exhausts. It is shown then that the asymptotic dynamics of the map is rather sensitive to initial conditions, which leads to coexistence of different metric attractors. We also investigate stability of trajectories representing Cournot equilibria, which in this case are not fixed but periodic points. In particular, it is shown that several such Cournot equilibria, belonging to different invariant manifolds, may coexist some of them being locally asymptotically stable and some being unstable.

Suggested Citation

  • 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.
    • Handle: RePEc:cst:wpaper:12
    as

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    File URL: http://www.gecomplexity-cost.eu/repec/cst/wpaper/geco_dp_12.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Puu, T. & Panchuk, A., 2009. "Oligopoly and stability," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2505-2516.
    4. Brianzoni, Serena & Michetti, Elisabetta & Sushko, Iryna, 2010. "Border collision bifurcations of superstable cycles in a one-dimensional piecewise smooth map," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(1), pages 52-61.
    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. 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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    multidimensional piecewise smooth map; coexisting metric attractors; oligopoly market model; Cournot equilibrium stability;
    All these keywords.

    JEL classification:

    • D41 - Microeconomics - - Market Structure, Pricing, and Design - - - Perfect Competition
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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