﻿ 双寡头价格博弈模型及其稳定性

# 双寡头价格博弈模型及其稳定性Duopoly Price Game Model and Its Stability

Abstract: Based on the adaptive decision-rule, the bounded rationality decision-making method and the delayed price-expectation, we constructed the price game model of differentiation products between two oligo- poly firms in this paper. Through extending the game model to the three-dimensional difference equation, we investigated the existence and stability of the fixed points of the price game model. The results show that the model has an unstable boundary fixed point and a local stable Nash equilibrium point, and the parameter conditions ensuring the local stability of Nash equilibrium point are given by employing the Jury’s criteria. Simulation experiments confirm that the price adjustment speed is the major factor influencing on the stabil-ity of Nash equilibrium point. The variations of weight in the adaptive decision-rule and in the delayed price- expectation all have slight influence on the stability of Nash equilibrium point. The price evolution will give birth to bifurcation and chaos when price adjustment speed takes bigger values. Maintaining lower price-ad-justment speed for the oligarchs with bounded rationality decision-making rule is a major route to avoid the chaotic variation of prices.

[1] L. Chen, G. R. Chen. Controlling chaos in an economic model. Physica A, 2007, 374(1): 349-358.

[2] H. N. Agiza, A. A. Elsadany. Chaotic dynamics in nonlinear duopoly game with heterogeneous players. Applied Mathematics and Computation, 2004, 149(3): 843-860.

[3] 陈国华, 李煜, 盛昭瀚. 基于不同决策规则的产出系统的混沌与控制[J]. 系统工程理论与实践, 2004, 24(5): 84-90.

[4] A. A. Elsadany. Dynamics of a delayed duopoly game with bounded rationality. Mathematical and Computer Modelling, 2010, 52(9-10): 1479-1489.

[5] 卢亚丽, 薛惠锋, 李战国. 一类经济博弈模型的复杂动力学分析及混沌控制[J]. 系统工程理论与实践, 2008, 28(4): 118- 123.

[6] H. N. Agiza, A. A. Elsadany. Nonlinear dynamics in the Cournot duopoly game with heterogeneous player. Physica A, 2003, 320: 512-524.

[7] W. J. Wu, Z. Q. Chen and W. H. Ip. Complex nonlinear dynamics and controlling chaos in a Cournot duopoly economic model. Nonlinear Analysis: Real World Applications, 2010, 11(5): 4363- 4377.

[8] J. A. Ho lyst, K. Urbanowicz. Chaos control in economical mo- del by time-delayed feedback method. Physica A, 2000, 287(3- 4): 587-598.

[9] J. G. Du, T. W. Huang, Z. H. Sheng and H. B. Zhang. A new method to control chaos in an economic system. Applied Mathe- matics and Computation, 2010, 217(6): 2370-2380.

[10] J. S. Cánovas, S. Paredes. On the control of some duopoly games. Mathematical and Computer Modelling, 2010, 52(7-8): 1110- 1115.

[11] E. Ahmed, M. F. Elettreby and A. S. Hegazi. On Puu’s incomplete information formulation for the standard and multi-team Bertrand game. Chaos, Solitons and Fractals, 2006, 30(5): 1180- 1184.

[12] B. G. Xin, T. Chen. On a master-slave Bertrand game model. Economic Modelling, 2011, 28(4): 1864-1870.

[13] J. X. Zhang, Q. L. Da and Y. H. Wang. The dynamics of Bertrand model with bounded rationality. Chaos, Solitons and Fractals, 2009, 39(5): 2048-2055.

[14] C. H. Tremblay, V. J. Tremblay. The Cournot-Bertrand model and the degree of product differentiation. Economics Letters, 2011, 111(3): 233-235.

[15] E. M. Elabbasy, H. N. Agiza and A. A. Elsadany. Analysis of nonlinear triopoly game with heterogeneous players. Computers and Mathematics with Applications, 2009, 57(3): 488-499.

[16] S. N. Elaydi. An introduction to difference equations. New York: Springer-Verlag Publishers, 1996.

[17] 吕金虎, 陆君安, 陈士华. 混沌时间序列分析及其应用[M].武汉: 武汉大学出版社, 2002.

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