This paper analyzes the chaotic dynamics of a quantum Cournot duopoly game with bounded rational players by applying quantum game theory. We investigate the impact of quantum entanglement on the stability of the quantum Nash equilibrium points and chaotic dynamics behaviors of the system. The result shows that the stability region decreases with the quantum entanglement increasing. The adjustment speeds of bounded rational players can lead to chaotic behaviors, and quantum entanglement accelerates the bifurcation and chaos of the system. Numerical simulations demonstrate the chaotic features via stability region, bifurcation, largest Lyapunov exponent, strange attractors, sensitivity to initial conditions and fractal dimensions.

中文翻译：

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有限理性量子古诺双头博弈的混沌动力学

本文运用量子博弈论分析了具有有限理性参与者的量子古诺双头博弈的混沌动力学。我们研究了量子纠缠对量子纳什平衡点稳定性和系统混沌动力学行为的影响。结果表明，稳定区随着量子纠缠的增加而减小。有限理性玩家的调整速度会导致混沌行为，而量子纠缠加速了系统的分岔和混沌。数值模拟通过稳定区域、分岔、最大李雅普诺夫指数、奇异吸引子、对初始条件的敏感性和分形维数证明了混沌特征。