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<p>Game theory primarily investigates the interactions between formalized incentive structures, functioning as a mathematical theory and methodology for analyzing phenomena with competitive or confrontational attributes. With the extension of quantum physics research findings to other scientific fields, game theory has been expanded into the quantum domain, giving rise to the emerging interdisciplinary discipline of quantum game theory. This study focuses on bounded-rational Cournot oligopoly games, incorporating inter-advertiser competition into the cost function. A delayed bounded-rational Cournot oligopoly game model is constructed, verifying that the proposed model is a complex dynamical system exhibiting bifurcation and chaos. It is further confirmed that the time delay effect influences inter-firm games, advancing the occurrence of bifurcation and chaos within the system. Additionally, after quantizing the model, the stability of equilibrium points is quantitatively analyzed based on dynamical system theory. By establishing the local stability conditions for Nash equilibrium, the model’s dynamic behaviors are qualitatively explored via simulation methods, including bifurcation diagrams and phase portraits. Our findings reveal that quantum entanglement significantly modulates the competitive dynamics among enterprises. Qualitative analysis demonstrates that increasing the degree of quantum entanglement advances the emergence of system bifurcation and chaos, thereby affecting the outcome of the game.</p>

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Dynamics of Quantum Double-Oligopoly Games Under Time-Delay Effects

  • 期刊论文

  • 发表日期：

    2026年7月26日

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  • Ping An,
  • Sheng-Bo Yin,
  • Jia-Hong Li,
  • Zheng Li

摘要

Game theory primarily investigates the interactions between formalized incentive structures, functioning as a mathematical theory and methodology for analyzing phenomena with competitive or confrontational attributes. With the extension of quantum physics research findings to other scientific fields, game theory has been expanded into the quantum domain, giving rise to the emerging interdisciplinary discipline of quantum game theory. This study focuses on bounded-rational Cournot oligopoly games, incorporating inter-advertiser competition into the cost function. A delayed bounded-rational Cournot oligopoly game model is constructed, verifying that the proposed model is a complex dynamical system exhibiting bifurcation and chaos. It is further confirmed that the time delay effect influences inter-firm games, advancing the occurrence of bifurcation and chaos within the system. Additionally, after quantizing the model, the stability of equilibrium points is quantitatively analyzed based on dynamical system theory. By establishing the local stability conditions for Nash equilibrium, the model’s dynamic behaviors are qualitatively explored via simulation methods, including bifurcation diagrams and phase portraits. Our findings reveal that quantum entanglement significantly modulates the competitive dynamics among enterprises. Qualitative analysis demonstrates that increasing the degree of quantum entanglement advances the emergence of system bifurcation and chaos, thereby affecting the outcome of the game.