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Stability, multi-stability and instability in Cournot duopoly game with knowledge spillover effects and relative profit maximization

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  • Li, Hui
  • Zhou, Wei
  • Elsadany, A. A
  • Chu, Tong

Abstract

A dynamic Cournot duopoly model with isoelastic demand function and knowledge spillover effects is established, in which the goals of two enterprises are relative profit maximization. Since these two enterprises only have incomplete information of the market, then it is assumed that the enterprises are boundedly rational, and they need to adjust their production decision in next period according to the gradient adjustment mechanism. Sufficient conditions for the existence and stable properties of unique Nash equilibrium can be judged with the help of the Jury criterion. The size of stability region is related to the values of parameters and the system has two different paths to chaos, one is via flip bifurcation and another is via Neimark-Sacker bifurcation. Finally, the complex dynamic characteristics also can be further studied by using numerical simulation, including the structures of multi-layer Arnold's tongues and coexistence of attractors.

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  • Li, Hui & Zhou, Wei & Elsadany, A. A & Chu, Tong, 2021. "Stability, multi-stability and instability in Cournot duopoly game with knowledge spillover effects and relative profit maximization," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    • Handle: RePEc:eee:chsofr:v:146:y:2021:i:c:s0960077921002903
    DOI: 10.1016/j.chaos.2021.110936
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    6. Li, Hui & He, Ruichun & Zhou, Wei, 2022. "Dynamic behaviors in a Cournot duopoly model with knowledge spillover effect based on constant conjectural variation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 305-323.
    7. 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).
    8. Xu, Lili & Matsumura, Toshihiro, 2022. "Welfare-reducing price competition under relative performance delegation with convex costs," Economic Modelling, Elsevier, vol. 112(C).
    9. Jumpei Hamamura, 2022. "Weight assigned to a rival's profit by an advantaged firm in relative performance evaluation with Cournot–Bertrand competition," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 43(7), pages 2838-2844, October.

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