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On the stability analysis of a delayed two-stage Cournot model with R&D spillovers

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  • Cao, Yang
  • Colucci, Renato
  • Guerrini, Luca

Abstract

We investigate the dynamics of Cournot’s duopoly model with time delays, where firms compete at the R&D level and settle on their quantity based on shared earnings at the second stage. Stability conditions of the equilibrium points and occurrence of Hopf bifurcations are analyzed. Furthermore, we present numerical simulations to furnish experimented evidence for the system’s complex behaviors.

Suggested Citation

  • Cao, Yang & Colucci, Renato & Guerrini, Luca, 2022. "On the stability analysis of a delayed two-stage Cournot model with R&D spillovers," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 543-554.
    • Handle: RePEc:eee:matcom:v:201:y:2022:i:c:p:543-554
    DOI: 10.1016/j.matcom.2021.03.007
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    References listed on IDEAS

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    1. Shibata, Takashi, 2014. "Market structure and R&D investment spillovers," Economic Modelling, Elsevier, vol. 43(C), pages 321-329.
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    3. Zhou, Jie & Zhou, Wei & Chu, Tong & Chang, Ying-xiang & Huang, Meng-jia, 2019. "Bifurcation, intermittent chaos and multi-stability in a two-stage Cournot game with R&D spillover and product differentiation," Applied Mathematics and Computation, Elsevier, vol. 341(C), pages 358-378.
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    5. Matsumura, Toshihiro & Matsushima, Noriaki & Cato, Susumu, 2013. "Competitiveness and R&D competition revisited," Economic Modelling, Elsevier, vol. 31(C), pages 541-547.
    6. Kamien, Morton I & Muller, Eitan & Zang, Israel, 1992. "Research Joint Ventures and R&D Cartels," American Economic Review, American Economic Association, vol. 82(5), pages 1293-1306, December.
    7. Wei Zhou & Xiao-Xue Wang, 2019. "On the Stability and Multistability in a Duopoly Game with R&D Spillover and Price Competition," Discrete Dynamics in Nature and Society, Hindawi, vol. 2019, pages 1-20, August.
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    Cited by:

    1. Culda, Loredana Camelia & Kaslik, Eva & Neamţu, Mihaela, 2022. "Stability and bifurcations in a general Cournot duopoly model with distributed time delays," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    2. Liu, Yifan & Cai, Jiazhi & Xu, Haowen & Shan, Minghe & Gao, Qingbin, 2023. "Stability and Hopf bifurcation of a love model with two delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 558-580.

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    Keywords

    Bifurcation; Cournot; Delay; R&D;
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