周玉峰, 滕志东. 双寡头垄断的非线性稳定性分析[J]. Journal of Xinjiang University (Natural Science Edition in Chinese and English), 2006, (1).DOI：
双寡头垄断的非线性稳定性分析
摘要
对非线性价格函数:P(D)=p0(1+1D)
用差分方程相关理论
分别对双寡头垄断的两种对策:古诺对策和斯坦克贝对策
研究了产量对策系统的稳定性.由于非线性函数形式复杂
这里借助计算机
运用D e lph i编写程序
并引进一个新的参数λ—单位最高风险比
讨论了λ的范围、初值的范围与系统稳定性的关系
得到了在一定条件下系统大范围渐近稳定的结论.
Abstract
In pertinency of a price function as nonlinear: P(D)=p_01+1D
by using the relevant theories of difference equations
we′ve obtained two mathematical games of duopoly oligopoly: Cournot game
Stackelberg game
and Prisoner game is adopted respectively in this paper for study and analysis on the stability of output decision-making system.Due to the complexity of nonlinear function in terms of the format
computer-aided methodology is employed by using Delphi for programming.A new parameter λ-the maximal unit risk ratio is introduced
and the relationship between the range of the scope of initial values and the stability of the system is discussed.The conclusion of globally asymptotic stability in the system has been drawn under the defined conditions.
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