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Systems 2018, 6(3), 30; https://doi.org/10.3390/systems6030030

Nonlinear Phenomena in Cournot Duopoly Model

Faculty and Informatics and Management, University of Hradec Králové, Rokitanského 62, 500 03 Hradec Králové, Czech Republic
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Received: 27 April 2018 / Revised: 24 June 2018 / Accepted: 9 July 2018 / Published: 13 July 2018
(This article belongs to the Special Issue Modelling of Economic Systems)
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Abstract

The economic world is very dynamic, and most phenomena appearing in this world are mutually interconnected. These connections may result in the emergence of nonlinear relationships among economic agents. Research discussions about different markets’ structures cannot be considered as finished yet. Even such a well-known concept as oligopoly can be described with different models applying diverse assumptions and using various values of parameters; for example, the Cournot duopoly game, Bertrand duopoly game or Stackelberg duopoly game can be and are used. These models usually assume linear functions and make analyses of the behavior of the two companies. The aim of this paper is to consider a nonlinear inverse demand function in the Cournot duopoly model. Supposing there is a sufficiently large proportion among the costs of the two companies, we can possibly detect nonlinear phenomena such as bifurcation of limit values of production or deterministic chaos. To prove a sensitive dependence on the initial condition, which accompanies deterministic chaos, the concept of Lyapunov exponents is used. We also point out the fact that even though some particular values of parameters are irrelevant for the above-mentioned nonlinear phenomena, it is worth being aware of their existence. View Full-Text
Keywords: bifurcation; the Cournot duopoly; Lyapunov exponents; nonlinear model; oligopoly bifurcation; the Cournot duopoly; Lyapunov exponents; nonlinear model; oligopoly
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Pražák, P.; Kovárník, J. Nonlinear Phenomena in Cournot Duopoly Model. Systems 2018, 6, 30.

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