Finance Discipline Group
UTS Business School
University of Technology, Sydney

Working Paper Series

Title:
The Birth of Limit Cycles in Nonlinear Oligopolies with Continuously Distributed Information Lags
Author(s): Carl Chiarella & Ferenc Szidarovszky
Date of publication: August 1999
Working paper number: 87
Abstract:
The dynamic behaviour 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.
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Comments: Published as: Chiarella, C. and Szidarovszky, F., 2005, "The Birth of Limit Cycles in Nonlinear Oligopolies with Continuously Distributed Information Lags", In Moshe Dror, Pierre L’Ecuyer and Ferenc Szidarovszky (eds) Modeling Uncertainty: An Examination of Stochastic Theory, Methods, and Applications, International Series in Operations Research & Management Science, Volume 46, 249.268.
Known citations:

Bischi, G., Chiarella, C., Kopel, M. and Szidarovszky, F., 2010, Nonliner Oligopolies: Stability and Bifuractions, Springer Verlag.

Chiarella, C. and Szidarovszky, F., 2001, "Dynamic Oligopolies, Stabilities and Bifurcations", CUBO: A Mathematical Journal, 3(2), 267-284.

Chiarella, C. and Szidarovszky, F., 2002, "The Asymptotic Behavior of Dynamic Rent-Seeking Games", Computers and Mathematics with Applications, 43(1-2), 169-178.

Chiarella, C. and Szidarovszky, F., 2003, "Bounded Continuously Distributed Delays in Dynamic Oligopolies", Chaos, Solitons and Fractals, 18(5), 977-993.

Chiarella, C. and Szidarovszky, F., 2004, "Dynamic Oligopolies Without Full Information and with Continuously Distributed Time Lags", Journal of Economic Behavior and Organization, 54(4), 495-511.

Chiarella, C. and Szidarovszky, F., 2005, "Cournot Oligopolies with Product Differentiation Under Uncertainty", Computers and Mathematics with Applications, 50(3-4), 413-424.

Chiarella, C. and Szidarovszky, F., 2008, "Dynamic Oligopolies with Production Adjustment Costs", Scientia Iranica, 15(1), 120-124.

Chiarella, C. and Szidarovszky, F., 2009, "Dynamic Oligopolies and Intertemporal Demand Interaction", CUBO: A Mathematical Journal, 11(2), 85-105.

Chiarella, C., Szidarovszky, F. and Zhu, P., 2002, "The Interaction of Uncertainty and Information Lags in the Cournot Oligopoly Model", In Tönu Puu and Irina Sushko (eds) Oligopoly Dynamics: Models and Tools, 233-263.

Engel, A., 2002, Dynamic Market Games with Time Delays and their Application to Internationa Fishing, PhD Thesis, University of Arizona.

Engel, A., Chiarella, C. and Szidarovszky, F., 2001, "A Game Theoretical Model of International Fishing with Time Delay", 2001 IEEE International Conference on Systems, Man, and Cybernetics, Tucson, Arizona, USA, 2658-2663.

Engel, A., Chiarella, C. and Szidarovszky, F., 2003, "A Game Theoretical Partially Cooperative Model of International Fishing with Time Delay", Chaos, Solitons and Fractals, 18(3), 549-560.

Engel, A., Chiarella, C. and Szidarovszky, F., 2007, "A Game Theoretical Coalition Model of International Fishing with Time Delay", Journal of Concrete and Applicable Mathematics, 5(2), 115-131.

Matsumoto, A., Chiarella, C. and Szidarovszky, F., 2013, "Dynamic Monopoly with Bounded Continuously Distributed Delay", Chaos, Solitons and Fractals, 47, 66-72.

Matsumoto, A. and Szidarovszky, F., 2003, "Dynamics in Delay Monopoly", Working Paper.

Matsumoto, A. and Szidarovszky, F., 2006, "Delayed Nonlinear Cournot and Bertrand Dynamics with Product Differentiation", Nonlinear Dynamics, Psychology and Life Sciences, 11(3), 367-395.

Matsumoto, A. and Szidarovszky, F., 2010, "Delayed Dynamics in Heterogeneous Competition with Product Differentiation", Nonlinear Analysis: Real World Applications, 11(2), 601-611.

Matsumoto, A. and Szidarovszky, F., 2012, "Nonlinear Delay Monopoly with Bounded Rationality", Chaos, Solitons and Fractals, 45(4), 507-519.

Matsumoto, A. and Szidarovszky, F., 2012, "Boundedly Rational Monopoly with Continuously Distributed Single Time Delay", Working Paper.

Matsumoto, A., Szidarovszky, F. and Yoshida, H., 2010, "Dynamics in Delay Cournot Duopoly", Working Paper.

Szidarovszky, F., Okuguchi, K. and Kopel, M., 2005, "International Fishery with Several Countries", PU.M.A., 16(4), 493-514.

Szidarovszky, F., Engel, A. and Chiarella, C., 2004, "A Game Theoretical Model of Model of International Fishing with Time Delay", International Game Theory Review, 6(3), 391.

Szidarovszky, F. and Chiarella, C., 2004, "The Ssymptotic Behavior of Dynamic Producer-Consumer Systems", Mathematical and Computer Modelling, 39(11-12), 1297-1312.