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On the Stability and Multistability in a Duopoly Game with R&D Spillover and Price Competition

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  • Wei Zhou
  • Xiao-Xue Wang

Abstract

In this paper, a dynamical two-stage game with R&D competition and joint profit maximization is built. The stability of all the equilibrium points is discussed through Jury condition, and the stability region of the Nash equilibrium point is then given. The influence of the parameters on the system is discussed, and we find that the firm can even benefit from chaos, when it has higher innovation efficiency and higher adjusting speed. And then the coexistence of multiple attractors is studied using basin of attraction. Our research result shows that the coexisting attractors can be observed in the two-parameter bifurcation diagram. At last, the boundary of feasible region, global bifurcations, and formation mechanism of fractal structure of attracting basin are analyzed through critical curves and noninvertible map theory.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnddns:2369898
    DOI: 10.1155/2019/2369898
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    Cited by:

    1. Yu, Yu & Yu, Weisheng, 2021. "The stability and duality of dynamic Cournot and Bertrand duopoly model with comprehensive preference," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    2. Liu, Yuxia & Zhou, Wei & Wang, Qian, 2022. "Global dynamics of an oligopoly competition model with isoelastic demand and strategic delegation," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    3. 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.
    4. Sameh S. Askar, 2020. "A Dynamic Duopoly Model: When a Firm Shares the Market with Certain Profit," Mathematics, MDPI, vol. 8(10), pages 1-13, October.
    5. Chu, Tong & Zhou, Wei, 2022. "Complex dynamics of R&D competition with one-way spillover based on intellectual property protection," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    6. 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).
    7. 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).

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