Table of Contents
Journal of Complex Systems
Volume 2014 (2014), Article ID 384843, 7 pages
http://dx.doi.org/10.1155/2014/384843
Research Article

Dynamic Cournot Duopoly Game with Delay

1Department of Basic Science, Faculty of Computers and Informatics, Suez Canal University, Ismailia, Egypt
2Department of Mathematics, Hail University, Hail, Saudi Arabia

Received 2 February 2014; Revised 24 May 2014; Accepted 25 May 2014; Published 19 June 2014

Academic Editor: Juan Luis Cabrera

Copyright © 2014 A. A. Elsadany and A. E. Matouk. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. G. I. Bischi, C. Chiarella, M. Kopel, and F. Szidarovszky, Nonlinear Oligopolies: Stability and Bifurcations, Springer, New York, NY, USA, 2009.
  2. A. Cournot, Research into the Principles of the Theory of Wealth, Irwin Paper Back Classics in Economics, Chapter 7, 1963.
  3. T. Puu, “Chaos in duopoly pricing,” Chaos, Solitons and Fractals, vol. 1, no. 6, pp. 573–581, 1991. View at Google Scholar · View at Scopus
  4. G.-I. Bischi, L. Stefanini, and L. Gardini, “Synchronization, intermittency and critical curves in a duopoly game,” Mathematics and Computers in Simulation, vol. 44, no. 6, pp. 559–585, 1998. View at Google Scholar · View at Scopus
  5. T. Puu, “The chaotic duopolists revisited,” Journal of Economic Behavior and Organization, vol. 33, no. 3-4, pp. 385–394, 1998. View at Google Scholar · View at Scopus
  6. E. Ahmed and H. N. Agiza, “Dynamics of a cournot game with n-competitors,” Chaos, Solitons and Fractals, vol. 9, no. 9, pp. 1513–1517, 1998. View at Google Scholar · View at Scopus
  7. H. N. Agiza, “On the analysis of stability, bifurcation, chaos and chaos control of Kopel map,” Chaos, Solitons and Fractals, vol. 10, no. 11, pp. 1909–1916, 1999. View at Publisher · View at Google Scholar · View at Scopus
  8. G. I. Bischi and A. Naimzada, “Global analysis of a dynamic duopoly game with bounded rationality,” in Advanced in Dynamic Games and Application, vol. 5, Chapter 20, pp. 361–385, Birkhäuser, Boston, Mass, USA, 2000. View at Google Scholar
  9. G. I. Bischi and M. Kopel, “Equilibrium selection in a nonlinear duopoly game with adaptive expectations,” Journal of Economic Behavior and Organization, vol. 46, no. 1, pp. 73–100, 2001. View at Publisher · View at Google Scholar · View at Scopus
  10. H. N. Agiza, A. S. Hegazi, and A. A. Elsadany, “The dynamics of Bowley's model with bounded rationality,” Chaos, Solitons and Fractals, vol. 12, no. 9, pp. 1705–1717, 2001. View at Publisher · View at Google Scholar · View at Scopus
  11. H. N. Agiza, A. S. Hegazi, and A. A. Elsadany, “Complex dynamics and synchronization of a duopoly game with bounded rationality,” Mathematics and Computers in Simulation, vol. 58, no. 2, pp. 133–146, 2002. View at Publisher · View at Google Scholar · View at Scopus
  12. F. Tramontana and A. E. A. Elsadany, “Heterogeneous triopoly game with isoelastic demand function,” Nonlinear Dynamics, vol. 68, no. 1-2, pp. 187–193, 2012. View at Publisher · View at Google Scholar · View at Scopus
  13. H. N. Agiza and A. A. Elsadany, “Nonlinear dynamics in the cournot duopoly game with heterogeneous players,” Physica A: Statistical Mechanics and Its Applications, vol. 320, pp. 512–524, 2003. View at Publisher · View at Google Scholar · View at Scopus
  14. H. N. Agiza and A. A. Elsadany, “Chaotic dynamics in nonlinear duopoly game with heterogeneous players,” Applied Mathematics and Computation, vol. 149, no. 3, pp. 843–860, 2004. View at Publisher · View at Google Scholar · View at Scopus
  15. J. Zhang, Q. Da, and Y. Wang, “Analysis of nonlinear duopoly game with heterogeneous players,” Economic Modelling, vol. 24, no. 1, pp. 138–148, 2007. View at Publisher · View at Google Scholar · View at Scopus
  16. T. Dubiel-Teleszynski, “Nonlinear dynamics in a heterogeneous duopoly game with adjusting players and diseconomies of scale,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 1, pp. 296–308, 2011. View at Publisher · View at Google Scholar · View at Scopus
  17. N. Angelini, R. Dieci, and F. Nardini, “Bifurcation analysis of a dynamic duopoly model with heterogeneous costs and behavioural rules,” Mathematics and Computers in Simulation, vol. 79, no. 10, pp. 3179–3196, 2009. View at Publisher · View at Google Scholar · View at Scopus
  18. F. Tramontana, “Heterogeneous duopoly with isoelastic demand function,” Economic Modelling, vol. 27, no. 1, pp. 350–357, 2010. View at Publisher · View at Google Scholar · View at Scopus
  19. H.-X. Yao and F. Xu, “Complex dynamics analysis for a duopoly advertising model with nonlinear cost,” Applied Mathematics and Computation, vol. 180, no. 1, pp. 134–145, 2006. View at Publisher · View at Google Scholar · View at Scopus
  20. J.-G. Du and T. Huang, “New results on stable region of Nash equilibrium of output game model,” Applied Mathematics and Computation, vol. 192, no. 1, pp. 12–19, 2007. View at Publisher · View at Google Scholar · View at Scopus
  21. A. K. Naimzada and L. Sbragia, “Oligopoly games with nonlinear demand and cost functions: two boundedly rational adjustment processes,” Chaos, Solitons and Fractals, vol. 29, no. 3, pp. 707–722, 2006. View at Publisher · View at Google Scholar · View at Scopus
  22. L. Chen and G. Chen, “Controlling chaos in an economic model,” Physica A: Statistical Mechanics and Its Applications, vol. 374, no. 1, pp. 349–358, 2007. View at Publisher · View at Google Scholar · View at Scopus
  23. J.-G. Du, T. Huang, and Z. Sheng, “Analysis of decision-making in economic chaos control,” Nonlinear Analysis: Real World Applications, vol. 10, no. 4, pp. 2493–2501, 2009. View at Publisher · View at Google Scholar · View at Scopus
  24. Z.-H. Sheng, T. Huang, J.-G. Du, Q. Mei, and H. Huang, “Study on self-adaptive proportional control method for a class of output models,” Discrete and Continuous Dynamical Systems B, vol. 11, no. 2, pp. 459–477, 2009. View at Publisher · View at Google Scholar · View at Scopus
  25. J. Ma and W. Ji, “Chaos control on the repeated game model in electric power duopoly,” International Journal of Computer Mathematics, vol. 85, no. 6, pp. 961–967, 2008. View at Publisher · View at Google Scholar · View at Scopus
  26. S. S. Askar, “Complex dynamic properties of Cournot duopoly games with convex and log-concave demand function,” Operations Research Letters, vol. 42, no. 1, pp. 85–90, 2014. View at Publisher · View at Google Scholar
  27. L. Zhao and J. Zhang, “Analysis of a duopoly game with heterogeneous players participating in carbon emission trading,” Nonlinear Analysis: Modelling and Control, vol. 19, no. 1, pp. 118–131, 2014. View at Google Scholar
  28. E. Ahmed, H. N. Agiza, and S. Z. Hassan, “On modifications of Puu's dynamical duopoly,” Chaos, Solitons and Fractals, vol. 11, no. 7, pp. 1025–1028, 2000. View at Publisher · View at Google Scholar · View at Scopus
  29. M. T. Yassen and H. N. Agiza, “Analysis of a duopoly game with delayed bounded rationality,” Applied Mathematics and Computation, vol. 138, no. 2-3, pp. 387–402, 2003. View at Publisher · View at Google Scholar · View at Scopus
  30. S. Z. Hassan, “On delayed dynamical duopoly,” Applied Mathematics and Computation, vol. 151, no. 1, pp. 275–286, 2004. View at Publisher · View at Google Scholar · View at Scopus
  31. A. A. Elsadany, “Dynamics of a delayed duopoly game with bounded rationality,” Mathematical and Computer Modelling, vol. 52, no. 9-10, pp. 1479–1489, 2010. View at Publisher · View at Google Scholar · View at Scopus
  32. L. U. Yali, “Dynamics of a delayed duopoly game with increasing marginal costs and bounded rationality strategy,” Procedia Engineering, vol. 15, pp. 4392–4396, 2011. View at Publisher · View at Google Scholar
  33. A. Matsumoto and F. Szidarovszky, “Nonlinear delay monopoly with bounded rationality,” Chaos, Solitons and Fractals, vol. 45, no. 4, pp. 507–519, 2012. View at Publisher · View at Google Scholar · View at Scopus
  34. A. Matsumoto and F. Szidarovszky, “Boundedly rational monopoly with continuously distributed single time delays,” IERCU Discussion Paper #180, 2012, http://www.chuo-u.ac.jp/chuo-u/ins_economics/pdf/f06_03_03_04/discussno180.pdf.
  35. A. Matsumoto and F. Szidarovszky, “Discrete-time delay dynamics of boundedly rational monopoly,” Decisions in Economics and Finance, vol. 37, no. 1, pp. 53–79, 2014. View at Publisher · View at Google Scholar · View at Scopus
  36. A. Matsumoto and F. Szidarovszky, “Complex dynamics of monopolies with gradient adjustment,” IERCU Discussion Paper #209.
  37. S. N. Elaydi, An Introduction to Difference Equations, Springer, New York, NY, USA, 1996.