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Mathematical properties of a discontinuous Cournot–Stackelberg model

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  • Tramontana, Fabio
  • Gardini, Laura
  • Puu, Tönu

Abstract

The object of this work is to perform the global analysis of a recent duopoly model which couples the two points of view of Cournot and Stackelberg [17,18]. The Cournot model is assumed with isoelastic demand function and unit costs. The coupling leads to discontinuous reaction functions, whose bifurcations, mainly border collision bifurcations, are investigated as well as the global structure of the basins of attraction. In particular, new properties are shown, associated with the introduction of horizontal branches, which differ significantly when the constant value is zero or positive and small. The good behavior of the model with positive constant is proved, leading to stable cycles of any period.

Suggested Citation

  • Tramontana, Fabio & Gardini, Laura & Puu, Tönu, 2011. "Mathematical properties of a discontinuous Cournot–Stackelberg model," Chaos, Solitons & Fractals, Elsevier, vol. 44(1), pages 58-70.
    • Handle: RePEc:eee:chsofr:v:44:y:2011:i:1:p:58-70
    DOI: 10.1016/j.chaos.2010.12.001
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    References listed on IDEAS

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    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, T., 1998. "The chaotic duopolists revisited," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 385-394, January.
    3. 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.
    4. Agliari, Anna & Chiarella, Carl & Gardini, Laura, 2006. "A re-evaluation of adaptive expectations in light of global nonlinear dynamic analysis," Journal of Economic Behavior & Organization, Elsevier, vol. 60(4), pages 526-552, August.
    5. Tramontana, Fabio, 2010. "Heterogeneous duopoly with isoelastic demand function," Economic Modelling, Elsevier, vol. 27(1), pages 350-357, January.
    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. Lamantia, Fabio & Pezzino, Mario & Scardamaglia, Bruno & Tramontana, Fabio, 2022. "A discontinuous model of duopoly with isoelastic demand and innovation costs," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    2. Sarah Mignot & Fabio Tramontana & Frank Westerhoff, 2024. "Complex dynamics in a nonlinear duopoly model with heuristic expectation formation and learning behavior," Annals of Operations Research, Springer, vol. 337(3), pages 809-834, June.

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