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Equilibria and their stability in an asymmetric duopoly model of Kopel

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  • Xiaoliang Li
  • Kongyan Chen

Abstract

In this paper, we investigate the equilibria and their stability in an asymmetric duopoly model of Kopel by using several tools based on symbolic computations. We explore the possible positions of the equilibria in Kopel's model. We discuss the possibility of the existence of multiple positive equilibria and establish a necessary and sufficient condition for a given number of equilibria to exist. Furthermore, if the two duopolists adopt the best response reactions or homogeneous adaptive expectations, we establish rigorous conditions for the existence of distinct numbers of positive equilibria for the first time.

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  • Xiaoliang Li & Kongyan Chen, 2023. "Equilibria and their stability in an asymmetric duopoly model of Kopel," Papers 2301.12628, arXiv.org.
    • Handle: RePEc:arx:papers:2301.12628
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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. Li, Bo & Liang, Houjun & Shi, Lian & He, Qizhi, 2022. "Complex dynamics of Kopel model with nonsymmetric response between oligopolists," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    3. Li, Xiaoliang & Wang, Dongming, 2014. "Computing equilibria of semi-algebraic economies using triangular decomposition and real solution classification," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 48-58.
    4. A. A. Elsadany & A. M. Awad, 2016. "Dynamical analysis and chaos control in a heterogeneous Kopel duopoly game," Indian Journal of Pure and Applied Mathematics, Springer, vol. 47(4), pages 617-639, December.
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