The Birth of Limit Cycles in Nonlinear Oligopolies with Continuously Distributed Information Lags

  • Carl Chiarella
  • Ferenc Szidarovszky
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 46)


The dynamic behavior of the output in nonlinear oligopolies is examined when the equilibrium is locally unstable. Continuously distributed time lags are assumed in obtaining information about rivals’ output as well as in obtaining or implementing information about the firms’ own output. The Hopf bifurcation theorem is used to find conditions under which limit cycle motion is born. In addition to the classical Cournot model, labor managed and rent seeking oligopolies are also investigated.


Modeling Uncertainty Bifurcation Parameter Price Function Rival Firm Good Response Function 
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  1. Arnold, V.I. (1978). Ordinary Differential Equations. MIT Press, Cambridge, MA.Google Scholar
  2. Carr, J. (1981). Applications of Center Manifold Theory. Springer-Verlag, New York.Google Scholar
  3. Chiarella, C. and A. Khomin. (1996). An Analysis of the Complex Dynamic Behavior of Nonlinear Oligopoly Models with Time Lags. Chaos, Solitons & Fractals, Vol. 7.No. 12, pp. 2049–2065.MathSciNetGoogle Scholar
  4. Cox, J.C. and M. Walker. (1998). Learning to Play Cournot Duopoly Strategies. J. of Economic Behavior and Organization, Vol. 36, pp. 141–161.Google Scholar
  5. Cushing, J.M. (1977). Integro-differential Equations and Delay Models in Population Dynamics. Springer-Verlag, Berlin/Heidelberg/New York.Google Scholar
  6. Guckenheimer, J. and P. Holmes. (1983). Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. Springer-Verlag, New York.Google Scholar
  7. Invernizzi, S. and A. Medio. (1991). On Lags and Chaos in Economic Dynamic Models. J. Math. Econ., Vol. 20, pp. 521–550.CrossRefMathSciNetGoogle Scholar
  8. Jackson, E.A. (1989). Perspectives of Nonlinear Dynamics. Vols. 1 & 2. Cambridge University Press.Google Scholar
  9. Kopel, M. (1996). Simple and Complex Adjustment Dynamics in Cournot Duopoly Models. Chaos, Solitons & Fractals, Vol. 7,No. 12, pp. 2031–2048.CrossRefMathSciNetGoogle Scholar
  10. Kubicek, M. and M. Marek. (1986). Computational Methods in Bifurcation Theory and Dissipative Structures. Springer-Verlag, Berlin/Heidelberg/New York.Google Scholar
  11. Miller, R.K. (1972). Asymptotic Stability and Peturbations for Linear Volterra Integrodifferential Systems. In Delay and Functional Differential Equations and Their Applications, edited by K. Schmitt. Academic Press, New York.Google Scholar
  12. Okuguchi, K. (1976). Expectations and Stability in Oligopoly Models. Springer-Verlag, Berlin/Heidelberg/New York.Google Scholar
  13. Okuguchi, K. and F. Szidarovszky. (1999). The Theory of Oligopoly with Multiproduct Firms. (2nd Edition) Springer-Verlag, Berlin/Heidelberg/New York.Google Scholar
  14. Russel, A.M., J. Rickard and T.D. Howroyd. (1986). The Effects of Delays on the Stability and Rate of Convergence to Equilibrium of Oligopolies. Econ. Record, Vol. 62, pp. 194–198.Google Scholar
  15. Szidarovszky, F. and S. Yakowitz. (1978). Principles and Procedures of Numerical Analysis. Plenum Press, New York/London.Google Scholar
  16. Volterra, V. (1931). Lecons sû la Théorie Mathématique de la Lutte pour la Vie. Gauthiers-Villars, Paris.Google Scholar

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  • Carl Chiarella
    • 1
  • Ferenc Szidarovszky
    • 2
  1. 1.School of Finance and EconomicsUniversity of Technology SydneyBroadwayAustralia
  2. 2.Department of Systems and Industrial EngineeringUniversity of Arizona TucsonArizonaUSA

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