Delayed duopoly game with adaptive and naive players

Based on the adaptive and naive assumption the model of duopoly game is formulated with time delay. The stability of fixed point is analyzed by rewriting the game model as a forth dimensional system and employing Jury's criteria. Numerical simulations are also provided to investigate the dynamical behavior of the game model. The results show that the Nash equilibrium point is asymptotically stable for any weights and within large region of initial value space.