基于差异化产品动态寡头博弈的系统动力学分析

System Dynamics Analysis of Dynamic Duopoly Game Based on Differentiated Products

以寡头企业具有有限理性和简单理性的产量调整行为和非线性成本函数为基础,论证了当横向产品差异度在一定范围内时,纳什均衡可作为稳定的动态均衡而实现.当超过一定范围时,利用数值模拟可观测到系统出现的周期性和混沌的复杂现象.在企业具有二次成本的假设条件下,研究了产品差异程度对纳什均衡稳定性的影响,得到了产品差异度越大,或市场竞争程度越低,系统的纳什均衡越不稳定的结论,表明了经济周期波动产生于非线性系统的内生性.与线性成本的对比说明,非线性成本缩小了纳什均衡的稳定域,增加了寡头市场的复杂性.研究也表明规模不经济的寡头厂商想通过增加产品差异度来减少竞争是有一定难度的.

In this paper,on the basis of duopolists with bounded and naive rationality,each firm has a nonlinear cost function.Nash equilibrium can be realized as a stable dynamic equilibrium when the speed of degree of product differentiation exists in a certain range.When it exceeds the certain range,periodic and chaotic complex phenomena of system by numerical simulation can be observed,which shows that endogencity of nonlinear system is responsible for economic periodic fluctuation.Under the assumption of quadratic cost of firms,the effect of degree of product differentiation on the stability of Nash equilibrium has been studied.We get the conclusion that a higher degree of product differentiation or a lower degree of market competition leads to a less stable Nash equilibrium of system,which shows fluctuations in economic cycle has produced from endogenous nonlinear system.The study also implies oligopoly firm with diseconomies of scale who wants to reduce competition by increasing the degree of product differentiation is futile has a certain degree of difficulty.