不同理性预期下Stackelberg模型的动态复杂性
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摘要
构建双寡头参与人分别采取有限理性和天真理性预期的Stackelberg博弈模型,研究市场均衡的稳定性条件及动态复杂性特征.通过理论求解和数值模拟得出结论:参与人在不完全信息和不同理性情况下,Stackelberg模型的参数取值范围决定了动态系统的稳定性、产量分岔、利润分岔、奇怪吸引子、吸引子维数和混沌等;如果参数取值满足一定条件,静态Stackelberg推测变差均衡能够实现;否则,Stackelberg推测变差均衡不稳定,非线性动态经济系统可能会出现周期变化或混沌的现象.
This paper established a dynamic Stackelberg model which assumed that the players have heterogeneous expectations one is bounded rationality and the other is naive expectation, and analyzed the stability condition of the equilibrium and the dynamic complexity of the model. By theory solution and numerical simulation, we can get the conclusion that when the players have incomplete information and heterogeneous expectations, the values of parameters determined the stability, the bifurcation of output,the bifurcation of profit, the strange attractors, the dimension of strange attractors and chaos of the dynamic system. Under certain conditions, Stackelberg conjectural variation equilibrium can be realized.Otherwise, the equilibrium of Stackelberg conjectural variation model will become unstable, and perioddoubling bifurcation or chaos will probably occur in the nonlinear dynamic economic system.
This paper established a dynamic Stackelberg model which assumed that the players have heterogeneous expectations one is bounded rationality and the other is naive expectation, and analyzed the stability condition of the equilibrium and the dynamic complexity of the model. By theory solution and numerical simulation, we can get the conclusion that when the players have incomplete information and heterogeneous expectations, the values of parameters determined the stability, the bifurcation of output,the bifurcation of profit, the strange attractors, the dimension of strange attractors and chaos of the dynamic system. Under certain conditions, Stackelberg conjectural variation equilibrium can be realized.Otherwise, the equilibrium of Stackelberg conjectural variation model will become unstable, and perioddoubling bifurcation or chaos will probably occur in the nonlinear dynamic economic system.
引文
[1]Bowley A L.The mathematical groundwork of economics[M].Oxford:Oxford University Press,1924.
[2]Frisch R.Monopole-polypole-la notion de force dans l'economie[M].Nationalokonomisk Tidsskrift,1933.
[3]王国成.西方经济学理性主义的嬗变与超越[J].中国社会科学,2012,33(7):68-81.Wang G C.Evolution and transcendence of rationalism in Western economics[J].Social Sciences in China,2012,33(7):68-81.
[4]Agiza H N,Hegazi A S,Elsadany A A.The dynamics of Bowley's model with bounded rationality[J].Chaos Solitons Fractals,2001,12(9):1705-1717.
[5]Elettreby M F,Mansour M.On Cournot dynamic multi-team game using incomplete information dynamical system[J].Applied Mathematics&Computation,2012,218(21):10691-10696.
[6]Peng J,Miao Z,Peng F.Study on a 3-dimensional game model with delayed bounded rationality[J].Applied Mathematics&Computation,2011,218(5):1568-1576.
[7]Elsadany A A.Dynamics of a delayed duopoly game with bounded rationality[J].Mathematical&Computer Modelling,2010,52(9-10):1479-1489.
[8]Yassen M T.Adaptive synchronization of Rossler and Lii systems with fully uncertain parameters[J].Chaos Solitons&Fractals,2005,23(23):1527-1536.
[9]Fanti L,Gori L.The dynamics of a differentiated duopoly with quantity competition[J].Economic Modelling,2012,29(2):421-427.
[10]Ding Z,Wang Q,Jiang S.Analysis on the dynamics of a Cournot investment game with bounded rationality[J].Economic Modelling,2014,39(39):204-212.
[11]Ahmed E,Elsadany A A,Pun T.On Bertrand duopoly game with differentiated goods[J].Applied Mathematics&Computation,2015,251(251):169-179.
[12]Ding Z,Li Q,Jiang S,et al.Dynamics in a Cournot investment game with heterogeneous players[J].Applied Mathematics&Computation,2015,256(C):939-950.
[13]姚洪兴,徐峰.双寡头有限理性广告竞争博弈模型的复杂性分析[J].系统工程理论与实践,2005,25(12):32-37.Yao H X,Xu F.Complex dynamics analysis for a duopoly advertising model with bounded rationality[J].Systems Engineering—Theory&Practice,2005,25(12):32-37.
[14]杜建国,盛昭瀚,姚洪兴.一类量本利模型的混沌表现评价[J].系统工程理论与实践,2005,25(6):94-99.Du J G,Sheng Z H,Yao H X.Performance measures of chaos for class of model of cost,sales volume and profits[J].Systems Engineering—Theory&Practice,2005,25(6):94-99.
[15]姚洪兴,吴承尧,刘新芝,等.一类金融古诺混沌模型的分析与控制[J].系统工程理论与实践,2007,27(5):55-62.Yao H X,Wu C Y,Liu X Z,et al.Analysis and control of chaos in a financial Cournot model[J].Systems Engineering—Theory&Practice,2007,27(5):55-62.
[16]张新华,赖明勇,叶泽.寡头发电商报价动态模型及其混沌控制[J].系统工程理论与实践,2009,29(5):83-91.Zhang X H,Lai M Y,Ye Z.Dynamic model for power bidding and its chaos control in oligopoly market[J].Systems Engineering—Theory&Practice,2009,29(5):83-91.
[17]徐峰,盛昭瀚,姚洪兴,等.延迟决策对一类双寡头广告博弈模型的影响分析[J].管理科学学报,2007,10(5):1-10.Xu F,Sheng Z H,Yao H X,et al.Study on a duopoly advertising model with delayed decisions[J].Journal of Management Sciences in China,2007,10(5):1-10.
[18]姚洪兴,王梅.动态Bertrand模型的复杂现象与混沌控制[J].陕西师范大学学报(自然科学版),2015,43(2):24-27.Yao H X,Wang M.The complex phenomena and the chaos control of Bertrand model[J].Journal of Shaanxi Normal University(National Science Edition),2015,43(2):24-27.
[19]于维生,董瑞,张志远.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[J].系统工程,2013,31(7):59-63.Yu W S,Dong R,Zhang Z Y.Complexity of the dynamic Stackelberg conjectural variation model with delayed bounded rationality[J].Systems Engineering,2013,31(7):59-63.
[20]胡荣,夏洪山.航空公司动态价格竞争复杂性及混沌控制——基于不同竞争战略与不同理性的分析[J].系统工程理论与实践,2013,33(1):151-158.Hu R,Xia H S.Complexity analysis and chaos control of airlines'dynamic price competition:An application of different competition strategies and heterogeneous players[J].Systems Engineering—Theory&Practice,2013,33(1):151-158.
[21]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,2013,30(2):126-137.Yu W S,Yu Y.The complexion of a dynamic duopoly game with bounded rationality based on conjectural variation of Bertrand model[J].The Journal of Quantitative&Technical Economics,2013,30(2):126-137.
[22]李仲飞,郑军,黄宇元.有限理性、异质预期与房价内生演化机制[J].经济学(季刊),2015,14(1):453-482.Li Z F,Zheng J,Huang Y Y.Bounded rationality,heterogeneous expectation and endogenous evolution mechanism of housing price[J].China Economic Quarterly,2015,14(1):453-482.
[23]张志远,于维生.有限理性行为规则下豪泰林模型的复杂性[J].系统工程理论与实践,2015,35(4):920-927.Zhang Z Y,Yu W S.Complexity of the Hotelling model with bounded rationality rules[J].Systems Engineering—Theory&Practice,2015,35(4):920-927.
[24]陈迅,赖纯见.区域房地产市场四方有限理性博弈研究[J].系统工程理论与实践,2016,36(4):857-874.Chen X,Lai C J.Research on the game of 4-player with bounded rationality in regional real estate market[J].Systems Engineering—Theory&Practice,2016,.36(4):857-874.
[25]Kaplan J L,Yorke J L.Chaotic behavior of multidimensional difference equations[M].New York:Springer,1979.
[2]Frisch R.Monopole-polypole-la notion de force dans l'economie[M].Nationalokonomisk Tidsskrift,1933.
[3]王国成.西方经济学理性主义的嬗变与超越[J].中国社会科学,2012,33(7):68-81.Wang G C.Evolution and transcendence of rationalism in Western economics[J].Social Sciences in China,2012,33(7):68-81.
[4]Agiza H N,Hegazi A S,Elsadany A A.The dynamics of Bowley's model with bounded rationality[J].Chaos Solitons Fractals,2001,12(9):1705-1717.
[5]Elettreby M F,Mansour M.On Cournot dynamic multi-team game using incomplete information dynamical system[J].Applied Mathematics&Computation,2012,218(21):10691-10696.
[6]Peng J,Miao Z,Peng F.Study on a 3-dimensional game model with delayed bounded rationality[J].Applied Mathematics&Computation,2011,218(5):1568-1576.
[7]Elsadany A A.Dynamics of a delayed duopoly game with bounded rationality[J].Mathematical&Computer Modelling,2010,52(9-10):1479-1489.
[8]Yassen M T.Adaptive synchronization of Rossler and Lii systems with fully uncertain parameters[J].Chaos Solitons&Fractals,2005,23(23):1527-1536.
[9]Fanti L,Gori L.The dynamics of a differentiated duopoly with quantity competition[J].Economic Modelling,2012,29(2):421-427.
[10]Ding Z,Wang Q,Jiang S.Analysis on the dynamics of a Cournot investment game with bounded rationality[J].Economic Modelling,2014,39(39):204-212.
[11]Ahmed E,Elsadany A A,Pun T.On Bertrand duopoly game with differentiated goods[J].Applied Mathematics&Computation,2015,251(251):169-179.
[12]Ding Z,Li Q,Jiang S,et al.Dynamics in a Cournot investment game with heterogeneous players[J].Applied Mathematics&Computation,2015,256(C):939-950.
[13]姚洪兴,徐峰.双寡头有限理性广告竞争博弈模型的复杂性分析[J].系统工程理论与实践,2005,25(12):32-37.Yao H X,Xu F.Complex dynamics analysis for a duopoly advertising model with bounded rationality[J].Systems Engineering—Theory&Practice,2005,25(12):32-37.
[14]杜建国,盛昭瀚,姚洪兴.一类量本利模型的混沌表现评价[J].系统工程理论与实践,2005,25(6):94-99.Du J G,Sheng Z H,Yao H X.Performance measures of chaos for class of model of cost,sales volume and profits[J].Systems Engineering—Theory&Practice,2005,25(6):94-99.
[15]姚洪兴,吴承尧,刘新芝,等.一类金融古诺混沌模型的分析与控制[J].系统工程理论与实践,2007,27(5):55-62.Yao H X,Wu C Y,Liu X Z,et al.Analysis and control of chaos in a financial Cournot model[J].Systems Engineering—Theory&Practice,2007,27(5):55-62.
[16]张新华,赖明勇,叶泽.寡头发电商报价动态模型及其混沌控制[J].系统工程理论与实践,2009,29(5):83-91.Zhang X H,Lai M Y,Ye Z.Dynamic model for power bidding and its chaos control in oligopoly market[J].Systems Engineering—Theory&Practice,2009,29(5):83-91.
[17]徐峰,盛昭瀚,姚洪兴,等.延迟决策对一类双寡头广告博弈模型的影响分析[J].管理科学学报,2007,10(5):1-10.Xu F,Sheng Z H,Yao H X,et al.Study on a duopoly advertising model with delayed decisions[J].Journal of Management Sciences in China,2007,10(5):1-10.
[18]姚洪兴,王梅.动态Bertrand模型的复杂现象与混沌控制[J].陕西师范大学学报(自然科学版),2015,43(2):24-27.Yao H X,Wang M.The complex phenomena and the chaos control of Bertrand model[J].Journal of Shaanxi Normal University(National Science Edition),2015,43(2):24-27.
[19]于维生,董瑞,张志远.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[J].系统工程,2013,31(7):59-63.Yu W S,Dong R,Zhang Z Y.Complexity of the dynamic Stackelberg conjectural variation model with delayed bounded rationality[J].Systems Engineering,2013,31(7):59-63.
[20]胡荣,夏洪山.航空公司动态价格竞争复杂性及混沌控制——基于不同竞争战略与不同理性的分析[J].系统工程理论与实践,2013,33(1):151-158.Hu R,Xia H S.Complexity analysis and chaos control of airlines'dynamic price competition:An application of different competition strategies and heterogeneous players[J].Systems Engineering—Theory&Practice,2013,33(1):151-158.
[21]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,2013,30(2):126-137.Yu W S,Yu Y.The complexion of a dynamic duopoly game with bounded rationality based on conjectural variation of Bertrand model[J].The Journal of Quantitative&Technical Economics,2013,30(2):126-137.
[22]李仲飞,郑军,黄宇元.有限理性、异质预期与房价内生演化机制[J].经济学(季刊),2015,14(1):453-482.Li Z F,Zheng J,Huang Y Y.Bounded rationality,heterogeneous expectation and endogenous evolution mechanism of housing price[J].China Economic Quarterly,2015,14(1):453-482.
[23]张志远,于维生.有限理性行为规则下豪泰林模型的复杂性[J].系统工程理论与实践,2015,35(4):920-927.Zhang Z Y,Yu W S.Complexity of the Hotelling model with bounded rationality rules[J].Systems Engineering—Theory&Practice,2015,35(4):920-927.
[24]陈迅,赖纯见.区域房地产市场四方有限理性博弈研究[J].系统工程理论与实践,2016,36(4):857-874.Chen X,Lai C J.Research on the game of 4-player with bounded rationality in regional real estate market[J].Systems Engineering—Theory&Practice,2016,.36(4):857-874.
[25]Kaplan J L,Yorke J L.Chaotic behavior of multidimensional difference equations[M].New York:Springer,1979.