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A Cournot triopoly with two identical producers

Author

Listed:
  • Alina Szuz

    (Independent researcher)

  • Anna Agliari

    (Catholic University of Sacred Heart)

  • Tonu Puu

    (Center for Regional Science, Umeå University, Umeå, Sweden)

Abstract

In the present paper we analyze a Cournot oligopoly with three competitors, and we assume that two of them behave in the same way. Therefore the game reduces to a duopoly competition. We assume an iso-elastic demand function derived from a Cobb-Douglas utility function and linear costs. Furthermore the competitors adjust their moves giving a weight ß to the best calculated reply and another ሺ1 − ß áˆ» for their own previous move. The adjustment process shows that the Cournot equilibrium point loses stability through a Neimark-Sacker bifurcation of subcritical type and this implies that diferent attractors may coexist. We show that the different attractors appear and/or disappear due to the occurrence of homoclinic and border collision bifurcations.

Suggested Citation

  • Alina Szuz & Anna Agliari & Tonu Puu, 2015. "A Cournot triopoly with two identical producers," Gecomplexity Discussion Paper Series 13, Action IS1104 "The EU in the new complex geography of economic systems: models, tools and policy evaluation", revised Aug 2015.
    • Handle: RePEc:cst:wpaper:13
    as

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

    as
    1. Anna Agliari & Laura Gardini & Tonu Puu, 2006. "Global Bifurcations In Duopoly When The Cournot Point Is Destabilized Via A Subcritical Neimark Bifurcation," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 1-20.
    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. 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.
    4. Foroni, Ilaria & Agliari, Anna, 2011. "Complex dynamics associated with the appearance/disappearance of invariant closed curves," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(8), pages 1640-1655.
    5. Rand, David, 1978. "Exotic phenomena in games and duopoly models," Journal of Mathematical Economics, Elsevier, vol. 5(2), pages 173-184, September.
    6. Medio,Alfredo & Lines,Marji, 2001. "Nonlinear Dynamics," Cambridge Books, Cambridge University Press, number 9780521551861, November.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Cournot oligopoly; two-dimensional piecewise discrete map; subcritical Neimark-Sacker bifurcation; homoclinic bifurcation.;
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