Chaotic dynamics and chaos control of cournot model with heterogenous players

Abstract

We analyze a Cournot duopoly game, where players have heterogeneous expectations and nonlinear cost function. Two types of players are considered: bounded rational and naive expectation. By using the theory of bifurcations of dynamical systems, the existence and stability for the equilibrium points of this system are obtained. Numerical simulations used to show bifurcations diagrams for various parameters and sensitive dependence on initial conditions. We observe that an increase of the players' speed of adjustment may change the stability of Nash equilibrium point and cause bifurcation and chaos to occur, and the system can return to stable state from chaotic state by delayed feedback chaos control method while suitable controlling factor is chosen. The analysis and results in this paper are interesting in mathematics and economics. © 2011 Springer-Verlag Berlin Heidelberg.