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Nonlinear Dynamics of Cournot Duopoly Game: When One Firm Considers Social Welfare

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  • S. S. Askar
  • A. A. Elsadany
  • Ya Jia

Abstract

In this paper, we study the competition between two firms whose outputs are quantities. The first firm considers maximization of its profit while the second firm considers maximization of its social welfare. Adopting a gradient-based mechanism, we introduce a nonlinear discrete dynamic map which is used to describe the dynamics of this game. For this map, the fixed points are calculated and their stability conditions are analyzed. This includes investigating some attracting set and chaotic behaviors for the complex dynamics of the map. We have also investigated the types of the preimages that characterize the phase plane of the map and conclude that the game’s map is noninvertible of type Z4−Z2.

Suggested Citation

  • S. S. Askar & A. A. Elsadany & Ya Jia, 2021. "Nonlinear Dynamics of Cournot Duopoly Game: When One Firm Considers Social Welfare," Discrete Dynamics in Nature and Society, Hindawi, vol. 2021, pages 1-11, January.
    • Handle: RePEc:hin:jnddns:6697341
    DOI: 10.1155/2021/6697341
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    Cited by:

    1. Culda, Loredana Camelia & Kaslik, Eva & Neamţu, Mihaela & Sîrghi, Nicoleta, 2024. "Dynamics of a discrete-time mixed oligopoly Cournot-type model with three time delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 226(C), pages 524-539.
    2. Zhu, Yan-lan & Zhou, Wei & Chu, Tong, 2022. "Analysis of complex dynamical behavior in a mixed duopoly model with heterogeneous goods," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).

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