Nonlinear dynamics in the Cournot duopoly game with heterogeneous   players
  We analyze a nonlinear discrete-time Cournot duopoly game, where players have heterogeneous expectations. Two types of players are considered: boundedly rational and naive expectations. In this study we show that the dynamics of the duopoly game with players whose beliefs are heterogeneous, may become complicated. The model gives more complex chaotic and unpredictable trajectories as a consequence of increasing the speed of adjustment of boundedly rational player. The equilibrium points and local stability of the duopoly game are investigated. As some parameters of the model are varied, the stability of the Nash equilibrium point is lost and the complex (periodic or chaotic) behavior occurs. Numerical simulations is presented to show that players with heterogeneous beliefs make the duopoly game behaves chaotically. Also we get the fractal dimension of the chaotic attractor of our map which is equivalent to the dimension of Henon map. 
H.N. Agiza and A. A. Elsadany