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A Dynamic Duopoly Model: When a Firm Shares the Market with Certain Profit

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  • Sameh S. Askar

    (Department of Statistics and Operations Research, College of Science, King Saud University, Riyadh 11451, Saudi Arabia
    Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt)

Abstract

The current paper analyzes a competition of the Cournot duopoly game whose players (firms) are heterogeneous in a market with isoelastic demand functions and linear costs. The first firm adopts a rationally-based gradient mechanism while the second one chooses to share the market with certain profit in order to update its production. It trades off between profit and market share maximization. The equilibrium point of the proposed game is calculated and its stability conditions are investigated. Our studies show that the equilibrium point becomes unstable through period doubling and Neimark–Sacker bifurcation. Furthermore, the map describing the proposed game is nonlinear and noninvertible which lead to several stable attractors. As in literature, we have provided an analytical investigation of the map’s basins of attraction that includes lobes regions.

Suggested Citation

  • Sameh S. Askar, 2020. "A Dynamic Duopoly Model: When a Firm Shares the Market with Certain Profit," Mathematics, MDPI, vol. 8(10), pages 1-13, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1826-:d:430636
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    References listed on IDEAS

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    Cited by:

    1. Askar, S.S., 2022. "Nonlinear dynamic investigations and global analysis of a Cournot duopoly game with two different objectives," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    2. Stanislav Stoykov & Ivan Kostov, 2023. "Price Competition with Differentiated Products on a Two-Dimensional Plane: The Impact of Partial Cartel on Firms’ Profits and Behavior," Games, MDPI, vol. 14(2), pages 1-25, March.
    3. Zhao, Ruijia & Song, Yunting & Wang, Haoze & Xie, Xinlian, 2022. "Bi-objective optimisation model and its exact solution method of profit and market share of novel repair-and-support ships based on game theory," Omega, Elsevier, vol. 113(C).

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