二次成本函数下的推测变差模型及其复杂性分析
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摘要
以寡头市场中两个企业进行产量竞争为基础,构造基于二次成本函数下推测变差的动力学模型并分析推测变差平衡点的稳定性.通过数值仿真的方法研究企业调整速度变化所产生的诸如分岔、混沌以及奇异吸引子等复杂动力学行为.得出随着调整速度的增加,系统将会从稳定状态转变成分岔状态甚至混沌,并且初值条件极小的变化都将导致产量产生剧烈的波动.此时企业需要将调整速度控制在一定范围内来调整自身产量才能最大化自身利润.一旦系统处于混沌状态,市场将会变得混乱.因此通过状态反馈和参数调整控制的方法对混沌进行控制使其形成新的稳定结构.
Based on the production competition between two firms in the oligopoly market,the paper proposes a dynamic model with conjectural variation under the quadratic cost function and analyzes the stability of conjectural variation equilibrium.Numerical simulation is used to study the complex behaviors generated by the speeds of output adjustment of firms,such as bifurcations,chaos,stranger attractors and so on.The results show that the system will change from a stable state into a bifurcation state even chaos with the increase of adjustment speed. Furthermore,a tiny variation of the initial value will cause drastic fluctuations in output.Firms need to control the adjustment speed within a certain range to adjust their output in order to maximize their profits.Once the system is in chaos,the market will become chaotic.Therefore,so chaos is controlled by state feedback and parameter adjustment to form a new stable structure.
Based on the production competition between two firms in the oligopoly market,the paper proposes a dynamic model with conjectural variation under the quadratic cost function and analyzes the stability of conjectural variation equilibrium.Numerical simulation is used to study the complex behaviors generated by the speeds of output adjustment of firms,such as bifurcations,chaos,stranger attractors and so on.The results show that the system will change from a stable state into a bifurcation state even chaos with the increase of adjustment speed. Furthermore,a tiny variation of the initial value will cause drastic fluctuations in output.Firms need to control the adjustment speed within a certain range to adjust their output in order to maximize their profits.Once the system is in chaos,the market will become chaotic.Therefore,so chaos is controlled by state feedback and parameter adjustment to form a new stable structure.
引文
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[10] 于维生,于羽.基于伯川德推测变差的有限理性动态寡头博弈的复杂性[J].数量经济技术经济研究,2013(2):126-137.
[11] 吴可菲,马军海.异质双寡头R&D竞争的复杂性分析[J].复杂系统与复杂性科学,2013(1):68-74.
[12] 张骥骧,达庆利,王延华.寡占市场中有限理性博弈模型分析[J].中国管理科学,2006(5):109-113.
[13] 张雅慧,周伟,黄萌佳,等.基于延迟决策和溢出效应的双寡头博弈稳定性[J].兰州交通大学学报,2018,37(1):119-124.
[14] 周伟,饶晓波,王晓雪.一类具有食物偏好的三种群生物模型的动力学分析[J].兰州交通大学学报,2014,33(3):46-53.
[15] 黄萌佳,周伟,杨琼,等.异质双寡头伯川德博弈模型的动力学分析[J].兰州交通大学学报,2018,37(1):15-21.
[16] GREBOGI C,OTT E,YORKE J A.Fractal basin boundaries,long-lived chaotic transients,and unstable-unstable pair bifurcation[J].Physical Review Letters,1983,51(10):935-938.
[2] BERTRAND J.Theorie mathematique de la richesse societe[J].Journal Des Savants,1883,67:499-08.
[3] YOUNG A A.Reviewed work:the mathematical groundwork of economics by A.L.Bowley[J].Journal of the American Statistical Association,1925,20(149):133-135.
[4] FRISH R.Monopoly,poly:the concept of force in the economys[J].International Economic Papers,1951,1:23-36.
[5] ZHANG J ,DA Q ,WANG Y .Analysis of nonlinear duopoly game with heterogeneous players[J].Economic Modelling,2007,24(1):138-148.
[6] AGIZA H N.On the analysis of stability,bifurcation,chaos and chaos control of kopel map[J].Chaos Solitons & Fractals,1999,10(11):1909-1916.
[7] ELABBASY E M,AGIZA H N,ELSADANY A A,et al.The dynamics of triopoly game with heterogeneous players[J].Int.J.Nonlinear Sci.,2007,3(2):83-90.
[8] DUBIEL-TELESZYNSKI T.Nonlinear dynamics in a heterogeneous duopoly game with adjusting players and diseconomies of scale[J].Communications in Nonlinear Science and Numerical Simulation,2011,16(1):296-308.
[9] YU W S,YU Y.A dynamic duopoly model with bounded rationality based on constant conjectural variation[J].Economic Modelling,2014,37:103-112.
[10] 于维生,于羽.基于伯川德推测变差的有限理性动态寡头博弈的复杂性[J].数量经济技术经济研究,2013(2):126-137.
[11] 吴可菲,马军海.异质双寡头R&D竞争的复杂性分析[J].复杂系统与复杂性科学,2013(1):68-74.
[12] 张骥骧,达庆利,王延华.寡占市场中有限理性博弈模型分析[J].中国管理科学,2006(5):109-113.
[13] 张雅慧,周伟,黄萌佳,等.基于延迟决策和溢出效应的双寡头博弈稳定性[J].兰州交通大学学报,2018,37(1):119-124.
[14] 周伟,饶晓波,王晓雪.一类具有食物偏好的三种群生物模型的动力学分析[J].兰州交通大学学报,2014,33(3):46-53.
[15] 黄萌佳,周伟,杨琼,等.异质双寡头伯川德博弈模型的动力学分析[J].兰州交通大学学报,2018,37(1):15-21.
[16] GREBOGI C,OTT E,YORKE J A.Fractal basin boundaries,long-lived chaotic transients,and unstable-unstable pair bifurcation[J].Physical Review Letters,1983,51(10):935-938.