不同理性预期下量子库诺特模型的动态演化分析

Analysis of the Dynamic Evolution of the Quantum Cournot Model Under Different Rational Expectations

针对库诺特双寡头量子纳什均衡的稳定性问题,利用量子博弈与非线性动力学理论,构建了不同理性预期下,以量子纠缠为变量的动态博弈模型,分析了模型的均衡解及稳定性条件。得出结论:量子均衡解在一定参数条件下是局部稳定的,企业预期调整速度会导致均衡解呈现复杂性特征,而量子纠缠可有效地控制其稳定性。对模型进行了数值分析,当参数不满足稳定性条件时会出现分岔、奇异吸引子等混沌现象。

Aiming at the stability of the Cournot duopoly quantum Nash equilibrium,using quantum game theory and nonlinear dynamics theory,a dynamic game model with quantum entanglement as a variable under different rational expectations is constructed.We analyze the equilibrium points and stability conditions of the model.It is concluded that the quantum equilibrium point is locally stable under certain parameter conditions.The adjustment speed of firm will cause the equilibrium point to exhibit complexity characteristics,and quantum entanglement can effectively control its stability.This paper makes a numerical simulation analysis of the model.When the parameters do not satisfy the stability conditions,chaotic characteristics such as bifurcation and strange attractors will appear.