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Cournot oligopoly when the competitors operate under capital constraints

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  • Merlone, Ugo
  • Szidarovszky, Ferenc

Abstract

In this paper we extend and generalize the interesting duopoly model proposed by Tönu Puu (1991). An n-firm oligopoly is considered without product differentiation, when the price function is hyperbolic and the production cost function is linear. It is assumed that in addition the firms have limited budgets to cover production costs, so if they exceed their budgets, then they have to borrow extra capital with given unit costs. This additional cost makes the payoff functions of the firms only piece-wise differentiable and the best response functions are not unimodal making the equilibrium analysis more complex than in the classical case. In this paper the mathematical model is first introduced and then the best response functions of the firms are determined. A graphical approach is shown to prove the existence of positive equilibrium. The stability of the equilibrium is examined in the simulation study.

Suggested Citation

  • Merlone, Ugo & Szidarovszky, Ferenc, 2022. "Cournot oligopoly when the competitors operate under capital constraints," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    • Handle: RePEc:eee:chsofr:v:160:y:2022:i:c:s0960077922003642
    DOI: 10.1016/j.chaos.2022.112154
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    References listed on IDEAS

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    1. Zhao, Jijun & Szidarovszky, Ferenc, 2008. "N-firm oligopolies with production adjustment costs: Best responses and equilibrium," Journal of Economic Behavior & Organization, Elsevier, vol. 68(1), pages 87-99, October.
    2. Merlone, Ugo & Szidarovszky, Ferenc, 2015. "Dynamic oligopolies with contingent workforce and investment costs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 108(C), pages 144-154.
    3. W. Bentley Macleod, 1985. "On Adjustment Costs and the Stability of Equilibria," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 52(4), pages 575-591.
    4. Akio Matsumoto & Ugo Merlone & Ferenc Szidarovszky, 2008. "Cartelizing Groups In Dynamic Linear Oligopoly With Antitrust Threshold," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 10(04), pages 399-419.
    5. Akio Matsumoto & Ugo Merlone & Ferenc Szidarovszky, 2010. "Cartelising Groups In Dynamic Hyperbolic Oligopoly With Antitrust Threshold," Australian Economic Papers, Wiley Blackwell, vol. 49(4), pages 289-300, December.
    6. Reynolds, Stanley S., 1991. "Dynamic oligopoly with capacity adjustment costs," Journal of Economic Dynamics and Control, Elsevier, vol. 15(3), pages 491-514, July.
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    8. Tönu Puu, 2018. "Disequilibrium Economics," Springer Books, Springer, number 978-3-319-74415-5, January.
    9. Szidarovszky, Ferenc & Yen, Jerome, 1995. "Dynamic Cournot oligopolies with production adjustment costs," Journal of Mathematical Economics, Elsevier, vol. 24(1), pages 95-101.
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    More about this item

    Keywords

    Oligopolies; Repeated games; Complex dynamics;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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