Abstract
The delay Cournot duopoly game is studied. Dynamical behaviors of the game are studied. Equilibrium points and their stability are studied. The results show that the delayed system has the same Nash equilibrium point and the delay can increase the local stability region.
Highlights
It is well known that the duopoly game is one of the fundamental oligopoly games [1, 2]
Agiza et al [10] examined the dynamical behavior of Bowley’s model with bounded rationality. They have studied the complex dynamics of bounded rationality duopoly game with nonlinear demand function [11]
Agiza and Elsadany [13, 14] were of the first authors who studied games with heterogeneous players, and in particular they analyze the dynamic behaviors emerging in this kind of games
Summary
It is well known that the duopoly game is one of the fundamental oligopoly games [1, 2]. Zhao and Zhang [27] studied a duopoly game with heterogeneous players participating in carbon emission trading and analyzed the asymptotic stability of the equilibrium points of the game. In these literatures, adjustment speed or other parameters are taken as bifurcation parameters, and complex results such as period doubling bifurcation, unstable period orbits, and chaos are found. We formulate a duopoly game with heterogeneous bounded rationality: one is boundedly rational player without delay and the other is delayed boundedly rational player and studying its dynamical behaviors.
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