Abstract
A dynamic Cournot duopoly game, characterized by firms with bounded rationality, is represented by a discrete-time dynamical system of the plane. Conditions ensuring the local stability of a Nash equilibrium, under a local (or myopic) adjustment process, are given, and the influence of marginal costs and speeds of adjustment of the two firms on stability is studied. The stability loss of the Nash equilibrium, as some parameter of the model is varied, gives rise to more complex (periodic or chaotic) attractors. The main result of this paper is given by the exact determination of the basin of attraction of the locally stable Nash equilibrium (or other more complex bounded attractors around it), and the study of the global bifurcations that change the structure of the basin from a simple to a very complex one, with consequent loss of predictability, as some parameters of the model are allowed to vary. These bifurcations are studied by the use of critical curves, a relatively new and powerful method for the study of noninvertible two-dimensional maps.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abraham, R., L. Gardini, and C. Mira. Chaos in Discrete Dynamical Systems (A Visual Introduction in Two Dimensions). Springer-Verlag, New York, 1996.
Bonanno, G. Oligopoly Equilibria When Firms Have Local Knowledge of Demand. International Economic Review, 29,45–55,1988.
Bonanno, G. and C. Zeeman. Limited Knowledge of Demand and Oligopoly Equilibria. Journal of Economic Theory, 35, 276–283, 1985.
Devaney, R. L. An Introduction to Chaotic Dynamical Systems. Benjamin/Cummings, Menlo Park, CA, 1987.
Dixit, A. Comparative Statics for Oligopoly. International Economic Review, 27, 107–122, 1986.
Fisher, F. M. The Stability of the Cournot Oligopoly Solution: The Effect of Speeds of Adjustment and Increasing Marginal Costs. Review of Economic Studies, 28,125–135, 1961.
Flam, S. D. Oligopolistic Competition: From Stability to Chaos. In: F. Gori, L. Geronazzo and M. Galeotti (eds.), Nonlinear Dynamics in Economics and Social Sciences. Lecture Notes in Economics and Mathematical Systems, vol. 399. pp. 232–237, Springer-Verlag, Berlin, 1993.
Furth, D. Stability and Instability in Oligopoly. Journal of Economic Theory, 40, 197–228, 1986.
Gumowski, I. and C. Mira. Dynamique Chaotique. Cepadues Editions, Toulose, 1980.
Hahn, F. The Stability of the Cournot Oligopoly Solution. Review of Economic Studies, 29, 329–331, 1962.
McManus, M. and R. E. Quandt. Comments on the Stability of the Cournot Oligopoly Model. Review of Economic Studies, 27, 136–139, 1961.
Mira, C, L. Gardini, A. Barugola, and J. C. Cathala. Chaotic Dynamics in Two-Dimensional Noninvertible Maps. World Scientific, Singapore, 1996.
Mira, C, D. Fournier-Prunaret, L. Gardini, H. Kawakami, and J. C. Cathala. Basin Bifurcations of Two-Dimensional Noninvertible Maps: Fractalization of Basins. International Journal of Bifurcations and Chaos, 4, 343–381, 1994.
Mira, C. and C. Rauzy. Fractal Aggregation of Basin Islands in Two-Dimensional Quadratic Noninvertible Maps. International Journal of Bifurcations and Chaos, 5, 991–1019, 1995.
Okuguchi, K. Adaptive Expectations in an Oligopoly Model. Review of Economic Studies, 37, 233–237, 1970.
Sacco, P. L. Adaptive Response and Cournotian Behavior. Economic Notes, 20,474–496, 1991.
Rosen, J. B. Existence and Uniqueness of Equilibrium Points for Concave n-Person Games. Econometrica, 33, 520–534, 1965.
Teocharis, R. D. On the Stability of the Cournot Solution of the Oligopoly Problem. Review of Economic Studies, 27, 133–134,1960.
Varian, H. R. Microeconomic Analysis, 3rd ed. W W. Norton, 1992.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Science+Business Media New York
About this paper
Cite this paper
Bischi, G.I., Naimzada, A. (2000). Global Analysis of a Dynamic Duopoly Game with Bounded Rationality. In: Filar, J.A., Gaitsgory, V., Mizukami, K. (eds) Advances in Dynamic Games and Applications. Annals of the International Society of Dynamic Games, vol 5. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-1336-9_20
Download citation
DOI: https://doi.org/10.1007/978-1-4612-1336-9_20
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-7100-0
Online ISBN: 978-1-4612-1336-9
eBook Packages: Springer Book Archive