专题论文

基于延迟决策双寡头Stackelberg博弈模型的混沌动力学研究

  • 肖悦 ,
  • 吴雪 ,
  • 彭煜
展开
  • 西南科技大学理学院, 绵阳 621010
肖悦,硕士研究生,研究方向为系统工程,电子信箱:xiaoyue@swust.edu.cn

收稿日期: 2017-10-30

  修回日期: 2018-04-02

  网络出版日期: 2018-04-27

Study on chaotic dynamics of a duopoly Stackelberg game with delayed strategies

  • XIAO Yue ,
  • WU Xue ,
  • PENG Yu
Expand
  • School of Science, Southwest University of Science and Technology, Mianyang 621010, China

Received date: 2017-10-30

  Revised date: 2018-04-02

  Online published: 2018-04-27

摘要

基于寡头垄断市场,建立了双寡头Stackelberg动态产量博弈模型。两家企业分别采用延迟决策的有限理性预期和自适应性预期,应用非线性动力学分析模型动态演化过程,运用稳定性理论分析Nash均衡解的稳定性,并通过数值模拟,从分岔、混沌和混沌控制等动力学行为研究了引入延迟策略的产量博弈模型。结果表明,适当的延迟系数能扩大系统稳定域。

本文引用格式

肖悦 , 吴雪 , 彭煜 . 基于延迟决策双寡头Stackelberg博弈模型的混沌动力学研究[J]. 科技导报, 2018 , 36(8) : 48 -54 . DOI: 10.3981/j.issn.1000-7857.2018.08.005

Abstract

In this paper, a duopoly Stackelberg game of output competition is built. The two players adopt different strategies, i.e. with the bounded rationality and with the adaptable expectation, respectively. For the duopoly Stackelberg model, a nonlinear dynamical system is used to analyze the time evolution and Nash equilibrium point are used to study its stability. Numerical simulations show a series of chaotic behaviors. The results demonstrate that a proper delay coefficient enlarges the stable region.

参考文献

[1] Cournot A A. Researches into the principles of the theory of wealth, irwin paper back classics in economics[M]. Paris:Hachette, 1963.
[2] Von Neumann J, Morgenstren O. Theory of games and economic behavior[M]. Princeton:Princeton University Press, 1944.
[3] Peng Yu, Lu Qian. Complex dynamics analysis for a duopoly Stackelberg game model with bounded rationality[J]. Applied Mathematics and Computation, 2015, 271(C):259-268.
[4] Elsadany A A. Dynamics of a delayed duopoly game with bounded rationality[J]. Mathematical and Computer Modelling, 2010, 52(9):1479-1489.
[5] Andaluz J, Jarne G. Stability of vertically differentiated Cournot and Bertrand-type models when firms are boundedly rational[J]. Annals of Operations Research, 2016, 238(1):1-25.
[6] Sarmah S P, Sinha S, Kumar L. Price and warranty competition in a duopoly distribution channel:Dynamic stability analysis for boundedly rational agents[J]. Ima Journal of Management Mathematics, 2015, 26(3):299-324.
[7] Shi Lian, Le Yun, Sheng Zhaohan. Analysis of price Stackelberg duopoly game with bounded rationality[J]. Discrete Dynamics in Nature and Society, 2014(2):1-8.
[8] Peng Yu, Lu Qian, Xiao Yue. A dynamic Stackelberg duopoly model with different strategies[J]. Chaos Solitons & Fractals, 2016, 85:128-134.
[9] Bashkirtseva I, Ryashko L, Ryazanova T. Stochastic sensitivity analysis of the variability of dynamics and transition to chaos in the business cycles model[J]. Communications in Nonlinear Science and Numerical Simulation, 2018, 54:174-184.
[10] Pecora L M, Carroll T L. Synchronization in chaotic systems[J]. Physics Review Letter, 1990, 64(8):821-824.
[11] Chen Diyi, Shi Lin, Chen Haitao, et al. Analysis and control of a hyper-chaotic system with only one nonlinear term[J]. Nonlinear Dynamics. 2012, 67(3):1745-1752.
[12] Zunino L, Rosso O A, Soriano M C. Characterizing the Hyperchaotic dynamics of a semiconductor laser subject to optical feedback via permutation entropy[J]. IEEE Journal of Selected Topics in Quantum Electronics, 2011, 17(5):1250-1257.
[13] Li Nianqiang, Pan Wei,Yan Lianshan, et al. On joint identification of the feedback parameters for hyper-chaotic systems:An optimization-based approach[J]. Chaos,Solitons& Fractals. 2011, 44(4):198-207.
[14] Sloth C, Esbensen T, Stoustrup J. Robust and fault-tolerant linear parameter-varying control of wind turbines[J]. Mechatronics, 2011, 21(4):645-659.
[15] Amer Y A. Resonance and vibration control of two-degree-offreedom nonlinear electromechanical system with harmonic excitation[J]. Nonlinear Dynamics, 2015, 81(4):2003-2019.
[16] Leonov G A, Kuznetsov N V, Korzhemanova N A, et al. Lyapunov dimension formula for the global attractor of the Lorenz system[J]. Communications in Nonlinear Science and Numerical Simulation, 2016, 41:84-103.
[17] Kuznetsov N V, Alexeeva T A, Leonov G A. Invariance of Lyapunov exponents and Lyapunov dimension for regular and irregular linearizations[J]. Nonlinear Dynamics, 2016, 85(1):195-201.
[18] Kunetsov S P, Pikovsky A. Autonomous coupled oscillators with hyperbolic strange attractors[J]. Physica D-nonlinear Phenomena, 2007, 232(2):87-102.
[19] Yassen M T, Agiza H Z. Analysis of a duopoly game with delayed bounded rationality[J]. Applied Mathematics and Computation, 2003, 138(2):387-402.
文章导航

/