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Triopoly Cournot–Bertrand Game Based on Fractional Bounded Rationality: Static and Dynamic Investigations

Author

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  • Mahmoud Awad
  • Mohamed Abouhawwash
  • S. S. Askar
  • H. N. Agiza
  • Florentino Borondo

Abstract

A triopoly game is introduced to study the competition among three firms in a single market, each operating in an oligopolistic market. Our study is concerned with a static model in which the market has taxes and a quadratic cost function in quantity. In the static system we employ, known as Cournot-Bertrand, one firm’s output depends on quantity, while the other firms’ outputs depend on price. In the first part of this paper, we study the existence of the Nash equilibrium and its condition of stability for the static mixed model. In the second part of this paper, we modify the standard bounded rationality to fractional bounded rationality of discrete dynamical systems that have increasing taxes according to quantities based on the Egyptian market. Finally, we present a numerical study of the dynamical system, demonstrating that a small degree of memory enhances system stability.

Suggested Citation

  • Mahmoud Awad & Mohamed Abouhawwash & S. S. Askar & H. N. Agiza & Florentino Borondo, 2024. "Triopoly Cournot–Bertrand Game Based on Fractional Bounded Rationality: Static and Dynamic Investigations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2024, pages 1-13, December.
    • Handle: RePEc:hin:jnddns:6622584
    DOI: 10.1155/2024/6622584
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