Analysis of Duopoly Output Game With Different Decision-Making Rules

Yali LU

Abstract


The main objective of this paper is to study the effects of output adjustment speed and weight on the dynamics and aggregate profits of a duopoly game model with heterogeneous players. In duopoly game process, one player chooses the bounded rationality strategy and the other adopts the adaptive expectation method. Also the linear inverse demand function and nonlinear cost function are used. The paper analyzes the stability of fixed points, and studies the dynamics of the duopoly model. Then an adaptive controller is constructed to maximize profits by controlling output chaos. Theoretical analysis and numerical simulations show that the duopoly game model has two equilibrium points: one is unstable and the other is locally stable. High output adjustment speed can cause chaotic variation of the outputs, which will decrease the profit of the firm with bounded rationality. The weight variation has little effect on inducing output chaos. The firm with bounded rationality has strong motives to suppress output chaos to maximize its profit. Numerical experiments to verify the effectiveness of the designed controller in this paper. From the profit point of view, the adaptive expectation method is better than the bounded rationality strategy.


Keywords


Duopoly game; Bounded rationality; Adaptive expectation; Chaos control; Numerical simulation

Full Text:

PDF

References


Agiza, A. A., Hegazi, A. S., & Elsadany, A. A. (2002). Complex dynamics and synchronization of a duopoly game with bounded rationality. Mathematics and Computers in Simulation, 58, 133–146.

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

Cánovas, J. S., & Paredes, S. (2010). On the control of some duopoly games. Mathematical and Computer Modelling, 52, 1110-1115.

Chen, L., & Chen, G. R. (2007). Controlling chaos in an economic model. Physica A, 374, 349–358.

Ding, Z. W., & Shi, G. P. (2009). Cooperation in a dynamical adjustment of duopoly game with incomplete information, chaos. Solitons and Fractals, 42, 989–993.

Du, J. G., Huang, T. W., & Sheng, Z. H. (2009). Analysis of decision-making in economic chaos control. Nonlinear Analysis: Real World Applications, 10, 2493-2501.

Du, J. G., Huang,T. W., Sheng, Z. H., & Zhang, H. B. (2010). A new method to control chaos in an economic system. Applied Mathematics and Computation, 217, 2370-

2380.

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

Jury, E. I., & Blanchard, J. (1961). A stability test for linear discrete systems in table form. Proc. Inst. Radio Eng., 49, 1947-1948.

Kamalinejad, H., Majd, V. J., Kebriaei, H., & Rahimi-Kian, A. (2010). Cournot games with linear regression expectations in oligopolistic markets. Mathematics and Computers in Simulation, 80, 1874-1885.

Naimzada, A., & Ricchiuti, G. (2011). Monopoly with local knowledge of demand function. Economic Modelling, 28, 299-307.

Ott, E., Grebogi, C., & Yorke, J. A. (1990). Controlling chaos. Physical Review Letters, 64, 1196-1199.

Yao, H. X., & Xu, F. (2006). Complex dynamics analysis for a duopoly advertising model with nonlinear cost. Applied Mathematics and Computation, 180, 134-145.

Yassen, M. T., & Agiza, H. N. (2003). Analysis of a duopoly game with delayed bounded rationality. Applied Mathematics and Computation, 138, 387-402.

Zhang, J. X., Da, Q. L., & Wang, Y. H. (2007). Analysis of nonlinear duopoly game with heterogeneous players. Economic Modelling, 24, 138-148.




DOI: http://dx.doi.org/10.3968/6117

Refbacks

  • There are currently no refbacks.


Copyright (c)



Share us to:   

Reminder

  • We are currently accepting submissions via email only.

    The registration and online submission functions have been disabled.

    Please send your manuscripts to mse@cscanada.net，or mse@cscanada.org  for consideration.

    We look forward to receiving your work.

 


We only use three mailboxes as follows to deal with issues about paper acceptance, payment and submission of electronic versions of our journals to databases:
caooc@hotmail.com; mse@cscanada.net; mse@cscanada.org

 Articles published in Management Science and Engineering are licensed under Creative Commons Attribution 4.0 (CC-BY).

 MANAGEMENT SCIENCE AND ENGINEERING Editorial Office

Address:1055 Rue Lucien-L'Allier, Unit #772, Montreal, QC H3G 3C4, Canada.

Telephone: 1-514-558 6138
Http://www.cscanada.net Http://www.cscanada.org

Copyright © 2010 Canadian Research & Development Centre of Sciences and Cultures