基于有界理性的非线性寡头动态价格博弈
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摘要
针对经济市场中的寡头竞争问题,建立一种非线性寡头动态价格竞争输出博弈模型,运用反向归纳法求解系统的纳什均衡解;基于有界理性预期进行决策,并对系统在不同参数条件下的情况进行数值仿真,分析倍周期分岔和混沌现象.仿真分析表明,基于参数变化的混沌控制方法可以控制动力系统的不稳定行为,促进了市场快速恢复稳定、有序的状态,为有效解决市场不稳定现象提供一种方法.
Aiming at the problem of oligopoly competition in economic market, a nonlinear oligopoly dynamic price competition output game model was established. The inverse induction method was used to solve the system's Nash equilibrium solution. The decision was based on the bounded rational expectation, and the numerical simulation of the system under different parameters was carried out to analyze the period-doubling bifurcation and chaos. The simulation analysis shows that the chaotic control method based on parameter variation can control the unstable behavior of the power system and promote the rapid recovery of the market in a stable and orderly state, which provides a method for effectively solving market instability.
Aiming at the problem of oligopoly competition in economic market, a nonlinear oligopoly dynamic price competition output game model was established. The inverse induction method was used to solve the system's Nash equilibrium solution. The decision was based on the bounded rational expectation, and the numerical simulation of the system under different parameters was carried out to analyze the period-doubling bifurcation and chaos. The simulation analysis shows that the chaotic control method based on parameter variation can control the unstable behavior of the power system and promote the rapid recovery of the market in a stable and orderly state, which provides a method for effectively solving market instability.
引文
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[2] DING Z,HANG Q,YANG H.Analysis of the dynamics of multi-team Bertrand game with heterogeneous players[M].Beijing:Taylor & Francis,2011:15-37.
[3] MOOREH L.Antoine-Augustin Cournot[J].Revue De Métaphysique Et De Morale,1905,13(3):521-543.
[4] 佟岩,王云,李爽.中小企业技术创新激励约束的博弈模型[J].沈阳大学学报(社会科学版),2014,16(3):304-307.TONG Y,WANG Y,LI S.Game model analysis of incentive and restriction of SMEs' technological innovation[J].Journal of Shenyang University(Social Science),2014,16(3):304-307.
[5] 林剑修.具有二期时滞的Bertrand混沌博弈研究[D].南昌:江西财经大学,2017.LIN J X.Research on the Bertrand chaotic games with two time delays[D].Nanchang:Jiangxi University of Finance & Economics,2017.
[6] MA J,PU X.The research on Cournot-Bertrand duopoly model with heterogeneous goods and its complex characteristics[J].Nonlinear Dynamics,2013,72(4):895-903.
[7] 彭靖.寡头垄断市场价格博弈模型复杂性及其应用研究[D].天津:天津大学,2010.PENG J.The complexity of price game model in oligopoly market and its application[D].Tianjin:Tianjin University,2010.
[8] ELSADANY A A,AGIZA H N,ELABBASY E M.Complex dynamics and chaos control of heterogeneous quadropoly game[J].Applied Mathematics & Computation,2013,219(24):11110-11118.
[9] 刘佳.电信业务市场竞争博弈过程解析及其复杂性研究[D].长春:吉林大学,2016.LIU J.Research on analyzing the process of competition game and its complexity in telecom business market[D].Changchun:Jilin University,2016.
[10] ANDALUZ J,ELSADANY A A,JARNE G.Nonlinear Cournot and Bertrand-type dynamic triopoly with differentiated products and heterogeneous expectations[M].Amsterdam:Elsevier Science Publishers B V,2017:22-46.
[11] 刘英英.时变时延离散网络控制系统的稳定性分析[J].沈阳大学学报(自然科学版),2015,27(4):301-305.LIU Y Y.Stability analysis for discrete-time networked control systems with time-varying delay[J].Journal of Shenyang University(Natural Science),2015,27(4):301-305.
[12] 杨红,陶冠男,张乐.一类时滞切换模糊系统的静态输出反馈控制[J].沈阳大学学报(自然科学版),2014,26(3):216-221.YANG H,TAO G N,ZHANG L.Static output feedback control for a class of time-delay switched fuzzy systems[J].Journal of Shenyang University(Natural Science),2014,26(3):216-221.