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Nonlinear dynamics of a duopoly Stackelberg game with marginal costs

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  • Yang, Xuenan
  • Peng, Yu
  • Xiao, Yue
  • Wu, Xue

Abstract

In this paper, the complex dynamics of a duopoly game with bounded rational players are investigated. The model of a dynamic production game is formulated in yield decision making process. A nonlinear Stackelberg system which describes the time evolution with marginal costs is analyzed and the stability situations of Nash equilibrium points are studied. Numerical simulations show a series of chaotic behaviors. The results demonstrate that complex dynamics of the game can be showed by simulating. As for the chaos emerged, effective method has been applied to force it back to stability.

Suggested Citation

  • Yang, Xuenan & Peng, Yu & Xiao, Yue & Wu, Xue, 2019. "Nonlinear dynamics of a duopoly Stackelberg game with marginal costs," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 185-191.
    • Handle: RePEc:eee:chsofr:v:123:y:2019:i:c:p:185-191
    DOI: 10.1016/j.chaos.2019.04.007
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    3. Yan, Bo & Ahmadi, Atefeh & Mehrabbeik, Mahtab & Rajagopal, Karthikeyan & He, Shaobo & Jafari, Sajad, 2022. "Expanding the duopoly Stackelberg game with marginal costs into a multipoly game with lowering the burden of mathematical calculations: a numerical analysis," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    4. Grau-Climent, Juan & Garcia-Perez, Luis & Alonso-Sanz, Ramon & Losada, Juan C., 2023. "Effect of players’ expectations and memory in a quantum Cournot game," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    5. Zhou, Die & Pi, Jinxiu & Yang, Guanghui & Yang, Hui, 2022. "Nonlinear dynamics of a heterogeneous quantum Commons’ tragedy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 608(P1).
    6. Tian, Baodan & Zhang, Yong & Li, Jiamei, 2020. "Stochastic perturbations for a duopoly Stackelberg model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    7. Zhang, Ming & Wang, Guanghui & Xu, Jin & Qu, Cunquan, 2020. "Dynamic contest model with bounded rationality," Applied Mathematics and Computation, Elsevier, vol. 370(C).
    8. Zongxian Wang & Xiao Li & Weihua Liang & Junhai Ma, 2023. "Does a New Electric Vehicle Manufacturer Have the Incentive for Battery Life Investment? A Study Based on the Game Framework," Mathematics, MDPI, vol. 11(16), pages 1-20, August.
    9. Peng, Yu & Xiao, Yue & Lu, Qian & Wu, Xue & Zhao, Yueru, 2020. "Chaotic dynamics in Cournot duopoly model with bounded rationality based on relative profit delegation maximization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(C).

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