双寡头价格博弈模型及其稳定性

Duopoly Price Game Model and Its Stability

摘要: 基于适应性决策规则，有限理性决策方法，延迟价格预期，构建了两寡头企业间有差异产品的价格博弈模型。通过把博弈模型扩阶为三维差分方程，研究了价格博弈模型不动点的存在性和稳定性。结果表明，该模型有一个不稳定的边界不动点和一个局部稳定的纳什平衡点，并通过Jury判据给出了纳什平衡点局部稳定的参数条件。仿真实验证实，价格调整速度是影响纳什平衡点稳定性的主要因素，适应性决策规则与延迟预期价格估计中的权重变化均对纳什平衡点的稳定性影响轻微。在价格调整速度较大时，价格演化会出现分岔与混沌现象。采用有限理性决策规则的寡头企业保持较低的价格调整速度是避免价格混沌变化的主要途径。

Abstract: Based on the adaptive decision-rule, the bounded rationality decision-making method and the delayed price-expectation, we constructed the price game model of differentiation products between two oligo- poly firms in this paper. Through extending the game model to the three-dimensional difference equation, we investigated the existence and stability of the fixed points of the price game model. The results show that the model has an unstable boundary fixed point and a local stable Nash equilibrium point, and the parameter conditions ensuring the local stability of Nash equilibrium point are given by employing the Jury’s criteria. Simulation experiments confirm that the price adjustment speed is the major factor influencing on the stabil-ity of Nash equilibrium point. The variations of weight in the adaptive decision-rule and in the delayed price- expectation all have slight influence on the stability of Nash equilibrium point. The price evolution will give birth to bifurcation and chaos when price adjustment speed takes bigger values. Maintaining lower price-ad-justment speed for the oligarchs with bounded rationality decision-making rule is a major route to avoid the chaotic variation of prices.