基于伯川德推测变差的有限理性动态寡头博弈的复杂性
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摘要
本文在具有伯川德(Bertrand)推测变差的推测变差模型的基础上,引入参与人的基本有限理性的动态产量调整行为,构建出动态调整系统,论证了企业调整速度在稳定域内时,静态伯川德推测变差均衡仍可作为稳定的动态均衡而实现。并用数值仿真的方法说明当企业的产量调整速度不在稳定域内时,经济系统将会出现倍周期分岔或混沌等复杂动态。
In this article,on the basis of conjectural variation model of Bertrand conjectural variation,it introduces a dynamic production adjustment behavior of basic bounded rationality to construct a dynamic adjustment system and demonstrates that static Bertrand conjectural variation equilibrium can be realized as a stable dynamic equilibrium under the assumption of adjustment speed in the stable region.We use numerical simulation to show that when production adjustment speed is not in stable region,there will be complex dynamics such as period-doubling bifurcation or chaos in economic system.
In this article,on the basis of conjectural variation model of Bertrand conjectural variation,it introduces a dynamic production adjustment behavior of basic bounded rationality to construct a dynamic adjustment system and demonstrates that static Bertrand conjectural variation equilibrium can be realized as a stable dynamic equilibrium under the assumption of adjustment speed in the stable region.We use numerical simulation to show that when production adjustment speed is not in stable region,there will be complex dynamics such as period-doubling bifurcation or chaos in economic system.
引文
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[3]Agiza H.N.,Hegazi A.S.,Elsadany A.A.,2002,Complex Dynamics and Synchronization of aDuopoly Game with Bounded Rationality[J],Mathematics and Computers in Simulation,58,133～146.
[4]Agiza H.N.,Elsadany A.A.,2004,Chaotic Dynamics in Nonlinear Duopoly Game with Heteroge-neous Players[J],Applied Mathematics and Computation,149,843～860.
[5]Elabbasy E.M.,Agiza H.N.,Elsadany A.A.,EL-Metwally H.,2007,The Dynamics of Tri-opoly Game with Heterogeneous Players[J],International Journal of Nonlinear Science,3,83～90.
[6]Jixiang Zhang,Qingli Da,Yanhua Wang,2007,Analysis of Nonlinear Duopoly Game with Hetero-geneous Players[J],Economic Modelling,24,138～148.
[7]Agiza H.N.,1998,Explicit Stability Zones for Cournot Game with3 and4 Competitors[J],Cha-os,Solitons and Fractals,9,1955～1966.
[8]Agiza H.N.,1999,On the Analysis of Stability,Bifurcation,Chaos and Chaos Control of KopelMap[J],Chaos,Solitons and Fractals,10,1909～1916.
[9]Kopel M.,1996,Simple and Complex Adjustment Dynamics in Cournot Duopoly Models[J],Cha-os,Solitons and Fractals,7,2031～2048.
[10]Agiza H.N.,Elsadany A.A.,2003,Nonlinear Dynamics in the Cournot Duopoly Game with Het-erogeneous Players[J],Physica A,320,512～524.
[11]Bowley A.L.,1924,The Mathematical Groundwork of Economics[M],Oxford University Press.
[12]Frisch R.,1951,Monopoly-Polypoly:The Concept of Force in the Economy[J],International E-conomic Papers,1,23～36.
[13]易余胤、盛昭瀚、肖条军:《具溢出效应的有限理性双寡头博弈的动态演化》[J],《系统工程学报》2004年第3期。
[14]张骥骧、达庆利:《双寡头不同理性博弈模型分析》[J],《东南大学学报(自然科学版)》2006年第6期。
[15]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年第5期。
[16]J.卡布尔:《产业经济学前沿问题》[M],中国税务出版社,北京腾图电子出版社,2000。
[2]Puu T.,1998,The Chaotic Duopolists Rrevisited[J],Journal of Economic Behavior and Organiza-tion,33,385～394.
[3]Agiza H.N.,Hegazi A.S.,Elsadany A.A.,2002,Complex Dynamics and Synchronization of aDuopoly Game with Bounded Rationality[J],Mathematics and Computers in Simulation,58,133～146.
[4]Agiza H.N.,Elsadany A.A.,2004,Chaotic Dynamics in Nonlinear Duopoly Game with Heteroge-neous Players[J],Applied Mathematics and Computation,149,843～860.
[5]Elabbasy E.M.,Agiza H.N.,Elsadany A.A.,EL-Metwally H.,2007,The Dynamics of Tri-opoly Game with Heterogeneous Players[J],International Journal of Nonlinear Science,3,83～90.
[6]Jixiang Zhang,Qingli Da,Yanhua Wang,2007,Analysis of Nonlinear Duopoly Game with Hetero-geneous Players[J],Economic Modelling,24,138～148.
[7]Agiza H.N.,1998,Explicit Stability Zones for Cournot Game with3 and4 Competitors[J],Cha-os,Solitons and Fractals,9,1955～1966.
[8]Agiza H.N.,1999,On the Analysis of Stability,Bifurcation,Chaos and Chaos Control of KopelMap[J],Chaos,Solitons and Fractals,10,1909～1916.
[9]Kopel M.,1996,Simple and Complex Adjustment Dynamics in Cournot Duopoly Models[J],Cha-os,Solitons and Fractals,7,2031～2048.
[10]Agiza H.N.,Elsadany A.A.,2003,Nonlinear Dynamics in the Cournot Duopoly Game with Het-erogeneous Players[J],Physica A,320,512～524.
[11]Bowley A.L.,1924,The Mathematical Groundwork of Economics[M],Oxford University Press.
[12]Frisch R.,1951,Monopoly-Polypoly:The Concept of Force in the Economy[J],International E-conomic Papers,1,23～36.
[13]易余胤、盛昭瀚、肖条军:《具溢出效应的有限理性双寡头博弈的动态演化》[J],《系统工程学报》2004年第3期。
[14]张骥骧、达庆利:《双寡头不同理性博弈模型分析》[J],《东南大学学报(自然科学版)》2006年第6期。
[15]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年第5期。
[16]J.卡布尔:《产业经济学前沿问题》[M],中国税务出版社,北京腾图电子出版社,2000。