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The Influences of Asymmetric Market Information on the Dynamics of Duopoly Game

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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

We investigate the complex dynamic characteristics of a duopoly game whose players adopt a gradient-based mechanism to update their outputs and one of them possesses in some way certain information about his/her opponent. We show that knowing such asymmetric information does not give any advantages but affects the stability of the game’s equilibrium points. Theoretically, we prove that the equilibrium points can be destabilized through Neimark-Sacker followed by flip bifurcation. Numerically, we prove that the map describing the game is noninvertible and gives rise to several stable attractors (multistability). Furthermore, the dynamics of the map give different shapes of quite complicated attraction basins of periodic cycles.

Suggested Citation

  • Sameh S. Askar, 2020. "The Influences of Asymmetric Market Information on the Dynamics of Duopoly Game," Mathematics, MDPI, vol. 8(7), pages 1-12, July.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:7:p:1132-:d:382841
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    References listed on IDEAS

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    Cited by:

    1. Jia Liu & Cuixia Li, 2023. "Dynamic Game Analysis on Cooperative Advertising Strategy in a Manufacturer-Led Supply Chain with Risk Aversion," Mathematics, MDPI, vol. 11(3), pages 1-24, January.
    2. Sameh S Askar & Abdulrahman Al-Khedhairi, 2020. "Local and Global Dynamics of a Constraint Profit Maximization for Bischi–Naimzada Competition Duopoly Game," Mathematics, MDPI, vol. 8(9), pages 1-16, August.

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