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A discontinuous model of duopoly with isoelastic demand and innovation costs

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  • Lamantia, Fabio
  • Pezzino, Mario
  • Scardamaglia, Bruno
  • Tramontana, Fabio

Abstract

The paper studies the dynamic properties of a duopoly game in which firms strategically compete in quality-enhancing innovation investments and quantities. Market demands are assumed to be isolastic (reciprocal to the price) functions. The non-linearity of the demand functions, as already highlighted by T. Puu in [11], suggests the existence of complicated dynamics (cyclical or chaotic) in a standard dynamic Cournot duopoly. In addition to this, competition in innovation introduces the presence of discontinuities in the best response functions, expanding the set of possible equilibria (including asymmetric and multiple ones) of the standard Cournot duopoly and further enriching the dynamic features of the model.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:chsofr:v:158:y:2022:i:c:s0960077922002259
    DOI: 10.1016/j.chaos.2022.112015
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    References listed on IDEAS

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    1. Bischi, Gian Italo & Kopel, Michael, 2001. "Equilibrium selection in a nonlinear duopoly game with adaptive expectations," Journal of Economic Behavior & Organization, Elsevier, vol. 46(1), pages 73-100, September.
    2. Dana, Rose-Anne & Montrucchio, Luigi, 1986. "Dynamic complexity in duopoly games," Journal of Economic Theory, Elsevier, vol. 40(1), pages 40-56, October.
    3. Puu, T., 1998. "The chaotic duopolists revisited," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 385-394, January.
    4. Andrew Eckert & Tilman Klumpp & Xuejuan Su, 2017. "An Equilibrium Selection Theory of Monopolization," Southern Economic Journal, John Wiley & Sons, vol. 83(4), pages 1012-1037, April.
    5. Lamantia, Fabio & Pezzino, Mario & Tramontana, Fabio, 2018. "Dynamic analysis of discontinuous best response with innovation," Journal of Economic Dynamics and Control, Elsevier, vol. 91(C), pages 120-133.
    6. 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.
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