Analysis of a Dynamical Cournot Duopoly Game with Distributed Time Delay

Nicoleta Sirghi, Mihaela Neamţu and Petru Claudiu Străin
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Mihaela Neamţu: Faculty of Economics and Business Administration, West University of Timisoara, Romania
Petru Claudiu Străin: Faculty of Mathematics and Informatics, West University of Timisoara, Romania

Timisoara Journal of Economics and Business, 2015, vol. 8, issue 1s, 1-13

Abstract: The aim of the paper is to analyze the dynamic model of the Cournot duopoly game with bounded rationality associated to two firms. We consider the cost function of the first firm as nonlinear and for the second firm as linear. The players do not have a complete knowledge of the market and they follow a bounded rationality adjustment process based on the estimation of the marginal profit. Also, the distributed time delay is introduced, because the decisions at the current time depend on the average past decisions. The mathematical model is described by a distributed delay differential system with two nonlinear equations. The study for the local stability of the Nash equilibrium point is carried out in the case of two types of kernels: weak (exponential) and Dirac. A change in local stability of the equilibrium point, from stable to unstable, implies a Hopf bifurcation. The delays are considered as bifurcation parameters. In some conditions of the parameters of the model, we have proved that a family of periodic solutions bifurcates from the equilibrium point when the bifurcation parameter passes through a critical value. Numerical simulations are performed to illustrate the effectiveness of our results. Finally, conclusions and future researches are provided.

Keywords: Cournot duopoly game; Cournot Model; Bounded Rationality; distributed time delay; local stability; Hopf bifurcation. (search for similar items in EconPapers)
JEL-codes: C61 C73 D43 D84 (search for similar items in EconPapers)
Date: 2015
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