非线性需求下四寡头价格博弈模型及其复杂特性

Four oligarchs price game model and its complex characteristics with nonlinear demand

针对实际竞争环境,建立寡头厂商成本相异和广义非线性需求的四寡头价格博弈模型.基于厂商采用不同决策规则的假设,利用复杂动力学原理,给出了价格博弈模型纳什均衡解.研究了系统稳定、倍周期分叉以及混沌的复杂特性,探讨了价格调整速度和初始条件对该离散系统动态演化过程的影响,以此为基础研究了寡头厂商的价格决策.研究结果表明,寡头厂商都应采用较低的价格调整速度,慎重选择博弈的初始条件.当现任寡头厂商迅速调整价格阻止新厂商进入,使得市场陷入混乱时,运用反馈控制方法可实现混沌控制.

In view of the actual competitive environment a four-oligarch price game model with variable costs and general nonlinear demand is established. Based on the hypothesis that vendors use different decision rules, using complex principle of dynamics the Nash equilibrium solutions are give. This paper studies the complex characteristics such as stability, the period-doubling bifurcation, and chaos. It also discusses the effects of price adjustment speed and initial conditions on the movement of the dynamic system, and the price decisions of oligarchs. The results show that the lower price adjustment speed should be taken, and initial conditions of the game must be chosen carefully. When the current oligarchs quickly adjust price in order to prevent a new oligarch from entering and market into chaos results, the delay feedback control method can be used to control the chaos.