延迟决策下动态斯坦科尔伯格推测变差模型及其复杂性分析
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摘要
以双寡头垄断市场中的两厂商都采取延迟有限理性预期规则进行产量调整为基础,构建动态斯坦科尔伯格推测变差模型。通过理论分析和数值模拟研究不同延迟系数下,动态产量调整系统的稳定性、分岔、吸引子、混沌等复杂特征。结果表明:延迟系数和参数取值会影响动态斯坦科尔伯格推测变差模型的稳定性,当参数不满足一定条件时,系统会发生倍周期分岔和出现混沌。
condidering the players use delayed bounded rationality to adjust their output,this paper establishes a dynamic Stackelberg conjectural variation model.Theory solutions and numerical simulations are provided to analyze the stability and dynamic complexity such as bifurcation,stranger attractors,and chaos of the nonlinear dynamic system.The results show that the coefficient of delayed and other parameters determined the stability of the dynamic Stackelberg conjectural variation model;and that when the parameters don’t meet certain conditions,the doubling-bifurcation and chaos will occur to the system.
condidering the players use delayed bounded rationality to adjust their output,this paper establishes a dynamic Stackelberg conjectural variation model.Theory solutions and numerical simulations are provided to analyze the stability and dynamic complexity such as bifurcation,stranger attractors,and chaos of the nonlinear dynamic system.The results show that the coefficient of delayed and other parameters determined the stability of the dynamic Stackelberg conjectural variation model;and that when the parameters don’t meet certain conditions,the doubling-bifurcation and chaos will occur to the system.
引文
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[3]Puu T.The chaotic duopolists revisited[J].Journal of Economic Behavior&Organization,1998,(37):385～394.
[4]Agiza H N,et al.The dynamics of Bowley’s model with bounded rationality[J].Chaos,Solitons and Fractals,2001,(12):1705～1717.
[5]Elettreby M F,Mansour M.On Cournot dynamic multi-team game using incomplete information dynamical system[J].Applied Mathematics and Computation,2012,(218):10691～10696.
[6]Jing P,et al.Study on a3-dimensional game model with delayed bounded rationality[J].Applied Mathe-matics and Computation,2011,(218):1568～1576.
[7]马军海,彭靖.延迟决策对一类寡头博弈模型的影响分析[J].系统工程学报,2010,(6):812～817.
[8]卢亚丽.主从型Bertrand价格博弈模型及其动力学分析[J].系统工程,2012,30(2):91～94.
[9]Yassen M T,et al.Analysis of a duopoly game with delayed bounded rationality[J].Applied Mathematics and Computation,2003(2/3),138:387～402.
[10]Elsadany A A.Dyanmics of a delayed duopoly game with bounded rationality[J].Mathematical and Computer Modelling,2010,52(9/10):1479～1489.
[11]姚洪兴,张芳.带时滞的多寡头古诺模型及其稳定性[J].系统工程,2011,29(11):115～118.
[12]J.卡布尔(于立译):产业经济学前沿问题[M].北京腾图电子出版社,2000.
[13]Kaplan J L,Yorke J L.Chaotic behavior of multidimensional difference equations[M].New York:Springer,1979.