Complex Dynamics Analysis of a Quantum Bertrand Duopoly Model with Heterogeneous Expectations

doi:10.12005/orms.2022.0182

Abstract

Abstract: In order to discuss the chaotic phenomenon of Bertrand duopoly game in economic system, based on the bounded rationality and naive expectation, the paper sets up a dynamic model of quantum Bertrand duopoly game by applying quantum game theory. We analyze the effect of quantum entanglement degree on stability of the equilibrium points and complex dynamics behaviors. The result shows that the quantum entanglement degree can enhance the stability of the system. The price adjustment speeds of the two firms can lead to complex chaotic characteristics of the system, the quantum entanglement degree can control the system's chaos. Numerical simulations demonstrate the correction of the theory via bifurcation, largest Lyapunov exponent, strange attractors, sensitivity to initial conditions and fractal dimensions.

Key words: quantum Bertrand duopoly game model, heterogeneous expectations, quantum entanglement degree, complex dynamics

摘要： 针对伯川德双寡头垄断博弈经济系统中出现的混沌现象,利用量子博弈论,构建了基于有限理性与天真预期行为的量子伯川德动态博弈模型,分析了量子纠缠度对纳什均衡点稳定性及复杂动力行为的影响。结果表明:量子纠缠度能增强该系统的稳定性,企业价格调整速度达到某一程度时会导致该系统的复杂混沌特性,纠缠度可以有效控制混沌状态。最后利用数值模拟从分岔、最大李雅普诺夫指数、奇怪吸引子、初始条件敏感性及分数维数方面验证了理论准确性。

关键词: 量子伯川德博弈模型, 异质性预期, 量子纠缠度, 复杂动力机制

CLC Number:

F224.32

ZHANG Xin-li, TIAN Ying-nan, WANG Jia-qi. Complex Dynamics Analysis of a Quantum Bertrand Duopoly Model with Heterogeneous Expectations[J]. Operations Research and Management Science, 2022, 31(6): 56-60.

张新立, 田英楠, 王嘉琪. 基于异质预期的量子伯川德博弈复杂动力机制分析[J]. 运筹与管理, 2022, 31(6): 56-60.

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