延迟有限理性下推测变差寡头博弈模型的复杂性
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摘要
在参与人具有延迟有限理性决策下,构造含有伯川德推测变差的动态寡头模型,对模型的推测变差均衡点的存在性和唯一性进行了证明,把企业的产量调整速度作为变量,分析企业的产量调整速度的变化产生的周期分岔、混沌等复杂行为,并对比了延迟理性和DFC方法的混沌控制效果.研究表明,尽管二者作用机理不同,但混沌现象都发生了延迟甚至消失,即系统的稳定性增强.
In this paper,we construct Bertrand dynamic duopoly model with conjectural variation.The existence and the uniqueness of conjectural variation equilibrium point of Bertrand model has been investigated;we consider the speed of production adjustment of firms as a variable and analyze the complex behaviors such as periodic bifurcation,chaos with the variation of the speed of production adjustment,and compared the effect of chaos control by delayed rationality and DFC method.The results show that although the two have different mechanisms,chaos phenomenon have delayed occurrence and even disappeared,that the stability of system enhanced.
In this paper,we construct Bertrand dynamic duopoly model with conjectural variation.The existence and the uniqueness of conjectural variation equilibrium point of Bertrand model has been investigated;we consider the speed of production adjustment of firms as a variable and analyze the complex behaviors such as periodic bifurcation,chaos with the variation of the speed of production adjustment,and compared the effect of chaos control by delayed rationality and DFC method.The results show that although the two have different mechanisms,chaos phenomenon have delayed occurrence and even disappeared,that the stability of system enhanced.
引文
[1]Bowley A L.The Mathematical Groundwork of Economics[M].Oxford University Press,1924.
[2]Frisch R.Monopoly-Polypoly-The concept of force in the economy,International Economic Papers[C].1951[1933],1:23-36.
[3]Cournot A.Recherches sur les Principes Mathematics de la Theorie de la Richesse[M].Hachette,1838.
[4]Agiza H N,Hegazi A S,Elsadany A A.The dynamics of Bowley's model with bounded rationality[J].Chaos,Solitons and Fractals,2001(12):1705-1717.
[5]Zhang J,Da Q,Wang Y.The dynamics of Bertrand model with bounded rationality[J].Chaos,Solitons and Fractals,2009(39):2048-2055.
[6]Dubiel-Teleszynski T.Nonlinear dynamics in a heterogeneous duopoly game with adjusting players and diseconomies of scale[J].Commun Nonlinear Sci Numer Simulat,2011(16):296-308.
[7]Agiza H N,Elsadany A A.Nonlinear dynamics in the Cournot duopoly game with heterogeneous players[J].Physica A,2003(320):512-524.
[8]Agiza H N,Elsadany A A.Chaotic dynamics in nonlinear duopoly game with heterogeneous players[J].Applied Mathematics and Computation,2004(149):843-860.
[9]Zhang J,Da Q,Wang Y.Analysis of nonlinear duopoly game with heterogeneous players[J].Economic Modelling,2007(24):138-148.
[10]Agiza H N.Explicit stability zones for cournot game with 3 and 4 competitors[J].Chaos,Solitons and Fractals,1998(9):1955-1966.
[11]Agiza H N.On the analysis of stability,bifurcation,chaos and chaos control of Kopel map[J].Chaos,Solitons and Fractals,1999(10):1909-1916.
[12]Elabbasy E M,Agiza H N,Elsadany A A,EL-Metwally H.The dynamics of triopoly game with heterogeneous players[J].International Journal of Nonlinear Science,2007(3):83-90.
[13]Elabbasy E M,Agiza H N,Elsadany A A.Analysis of nonlinear triopoly game with heterogeneous players[J].Computers and Mathematics with Applications,2009(57):488-499.
[14]Ahmed E,Agiza H N,Hassan S Z.On modifications of Puu's dynamical duopoly[J].Chaos,Solitons and Fractals,2000(11):1025-1028.
[15]Yassen M T,Agiza H N.Analysis of a duopoly game with delayed bounded rationality[J].Applied Mathematics and Computation,2003(138):387-402.
[16]Elsadany A A.Dynamics of a delayed duopoly game with bounded rationality[J].Mathematical and Computer Modelling,2010(52):1479-1489.
[17]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,2010,25(6):812-817.
[18]徐峰,盛昭瀚,姚洪兴,陈国华.具溢出效应的有限理性双寡头博弈的动态演化[J].管理科学学报,2007,10(5):1-10.
[19]Pyragas K.Experimental control of chaos by delayed self-controlling feedback[J].Physics Letters A,1993,180(1):99-102.
[2]Frisch R.Monopoly-Polypoly-The concept of force in the economy,International Economic Papers[C].1951[1933],1:23-36.
[3]Cournot A.Recherches sur les Principes Mathematics de la Theorie de la Richesse[M].Hachette,1838.
[4]Agiza H N,Hegazi A S,Elsadany A A.The dynamics of Bowley's model with bounded rationality[J].Chaos,Solitons and Fractals,2001(12):1705-1717.
[5]Zhang J,Da Q,Wang Y.The dynamics of Bertrand model with bounded rationality[J].Chaos,Solitons and Fractals,2009(39):2048-2055.
[6]Dubiel-Teleszynski T.Nonlinear dynamics in a heterogeneous duopoly game with adjusting players and diseconomies of scale[J].Commun Nonlinear Sci Numer Simulat,2011(16):296-308.
[7]Agiza H N,Elsadany A A.Nonlinear dynamics in the Cournot duopoly game with heterogeneous players[J].Physica A,2003(320):512-524.
[8]Agiza H N,Elsadany A A.Chaotic dynamics in nonlinear duopoly game with heterogeneous players[J].Applied Mathematics and Computation,2004(149):843-860.
[9]Zhang J,Da Q,Wang Y.Analysis of nonlinear duopoly game with heterogeneous players[J].Economic Modelling,2007(24):138-148.
[10]Agiza H N.Explicit stability zones for cournot game with 3 and 4 competitors[J].Chaos,Solitons and Fractals,1998(9):1955-1966.
[11]Agiza H N.On the analysis of stability,bifurcation,chaos and chaos control of Kopel map[J].Chaos,Solitons and Fractals,1999(10):1909-1916.
[12]Elabbasy E M,Agiza H N,Elsadany A A,EL-Metwally H.The dynamics of triopoly game with heterogeneous players[J].International Journal of Nonlinear Science,2007(3):83-90.
[13]Elabbasy E M,Agiza H N,Elsadany A A.Analysis of nonlinear triopoly game with heterogeneous players[J].Computers and Mathematics with Applications,2009(57):488-499.
[14]Ahmed E,Agiza H N,Hassan S Z.On modifications of Puu's dynamical duopoly[J].Chaos,Solitons and Fractals,2000(11):1025-1028.
[15]Yassen M T,Agiza H N.Analysis of a duopoly game with delayed bounded rationality[J].Applied Mathematics and Computation,2003(138):387-402.
[16]Elsadany A A.Dynamics of a delayed duopoly game with bounded rationality[J].Mathematical and Computer Modelling,2010(52):1479-1489.
[17]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,2010,25(6):812-817.
[18]徐峰,盛昭瀚,姚洪兴,陈国华.具溢出效应的有限理性双寡头博弈的动态演化[J].管理科学学报,2007,10(5):1-10.
[19]Pyragas K.Experimental control of chaos by delayed self-controlling feedback[J].Physics Letters A,1993,180(1):99-102.