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The Interaction of Uncertainty and Information Lags in the Cournot Oligopoly Model

Chapter

Abstract

The Cournot oligopoly model is one of the classical models of the economic dynamics literature. The pioneering work of Cournot (1838) initiated a large sequence of studies on static and dynamic models. Okuguchi (1976) discusses single-product models and also gives a comprehensive literature review, particularly of stability conditions. Okuguchi and Szidarovszky (1999) extend the analysis to allow for oligopolies consisting of multi-product firms. Many existing oligopoly models assume perfect knowledge by firms of the market demand functions as well as of the firm’s own cost function. While perfect knowledge of the cost functions seems to be a realistic assumption, that of the demand functions may be less so. There have been only some limited attempts at modelling inaccurate knowledge of the demand function in oligopolies. Cyert and DeGroot (1971, 1973) have examined duopoly models. Kirman (1975) considered differentiated products and linear demand functions which firms misspecify and attempt to estimate. The resulting process may converge to the full information equilibrium or to some other equilibria. He also analysed how the resulting equilibrium values are affected (Kirman, 1983). Gates et al. (1982) have considered linear demand functions and differentiated products and assumed some economically guided learning process. Shapiro (1989) has discussed the use of trigger price strategies. Szidarovszky and Okuguchi (1990) have analysed the asympotic stability of oligopolies with perceived marginal costs. Léonard and Nishimura (1999) considered a discrete dynamic duopoly with linear cost functions and illustrated how the fundamental dynamic properties of the model are drastically altered as a result of the lack of full information on the demand functions.

Keywords

Bifurcation Diagram Demand Function Inverse Demand Function Firm Case Linear Cost Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Chiarella, C. and A. Khomin, 1996, “An Analysis of the Complex Dynamic Behaviour of Nonlinear Oligopoly Models with Time Lags”, Chaos, Solitons of Fractals, Vol. 7, No. 2, 2049–2065CrossRefGoogle Scholar
  2. Chiarella, C. and F. Szidarovszky, 2001, “The Birth of Limit Cycles in Non-linear Oligopolies with Continuously Distributed Information Lags”, In Modeling Uncertainty ( M. Dror editor), Kluwer Academic Publishers, DordrechtGoogle Scholar
  3. Cournot, A., 1938, Recherches sur les Principes Mathèmatiques de la Thèorie de Richesses, Hachette, Paris (English translation (1960), Researches into the Mathematical Principles of the Theory of Wealth, Kelley, New York )Google Scholar
  4. Cyert, R. M. and M. H. DeGroot, 1971, “Interfirm Learning and the Kinked Demand Curve”, Journal of Economic Theory, Vol. 3Google Scholar
  5. Cyert, R. M. and M. H. DeGroot, 1973, “An Analysis of Cooperation and Learning in a Duopoly Context”, American Economic Review, Vol. 63Google Scholar
  6. Gates, D. J., J. A. Rickard and M. Westcott, 1982, “Exact Cooperative Solutions of a Duopoly Model without Cooperation”, Journal of Mathematical Economics, Vol. 9, 27–35CrossRefGoogle Scholar
  7. Guckenheimer, J. and P. Holmes, 1983, Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Springer - Verlag, New YorkGoogle Scholar
  8. Invernizzi S. and A. Medio, 1991, “On Lags and Chaos in Economic Models”, Journal Mathematical Economics, Vol. 20, 52 1550Google Scholar
  9. Jin, J. Y., 2001, “Monopolistic Competition and Bounded Rationality”, Journal of Economic Behaviour and Organization, Vol. 45, 175–184CrossRefGoogle Scholar
  10. Kirman, A., 1975, “Learning by Firms about Demand Conditions”, In: Adaptive Economic Models ( R. H. Day and T. Groves, eds.), Academic Press, New YorkGoogle Scholar
  11. Kirman, A., 1983, “On Mistaken Beliefs and Resultant Equilibria”, In: Individual Forecasting and Aggregate Outcomes ( R. Frydman and E. S. Phelps, eds.), Cambridge University Press, New YorkGoogle Scholar
  12. Kopel, M., 1996, “Simple and Complex Adjustment Dynamics in Cournot Duopoly Models”, Chaos, Solitions and Fractals, Vol. 7, No. 12, 2031–2048CrossRefGoogle Scholar
  13. Léonard D., and K. Nishimura, 1999, “Nonlinear Dynamics in the Cournot Model without Full Information”, Annals of Operations Research, Vol. 89, 165–173CrossRefGoogle Scholar
  14. Okuguchi, K., 1976, Expectations and Stability in Oligopoly Models. Springer-Verlag, Berlin/ Heidelberg/ New YorkCrossRefGoogle Scholar
  15. Okuguchi, K. and F. Szidarovszky, 1999, The Theory of Oligopoly with Multi-Product Firms (2’ d edition), Springer-Verlag, Berlin/ Heidelberg/ New YorkCrossRefGoogle Scholar
  16. Puu, T., 2000, Attractors, Bifurcations, and Chaos: Nonlinear Phenomena in Economics. Springer-Verlag, Berlin/ Heidelberg/ New YorkGoogle Scholar
  17. 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”, Economic Record, Vol. 62, 194–198CrossRefGoogle Scholar
  18. Shapiro, C., 1989, “Theories of Oligopoly Behavior`, In: Handbook of Industrial Organization ( R. Schmalensee and R. D. Willig, eds.), North Holland, AmsterdamGoogle Scholar
  19. Szidarovszky, F. and K. Okuguchi, 1990, “Dynamic Oligopoly: Models with Incomplete Information”, Applied Mathematics and Computation, Vol. 38, No. 2, 161–177CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  1. 1.School of Finance and EconomicsUniversity of TechnologySydneyAustralia
  2. 2.Systems and Industrial Engineering DepartmentUniversity of ArizonaUSA

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