Complex dynamics analysis for a duopoly Stackelberg game model with bounded rationality

In view of the effect of differences between plan products and actual products, a duopoly Stackelberg model of competition on output is formulated. The firms announce plan products sequentially in planning phase and act simultaneously in production phase. Backward induction is used to solve subgame Nash equilibrium. The equilibrium outputs and equilibrium profits are affected by cost coefficients. For the duopoly Stackelberg model, a nonlinear dynamical system which describes the time evolution with bounded rationality is analyzed. The equilibria of the corresponding discrete dynamical systems are investigated. The local stability analysis has been carried out. The stability of Nash equilibrium gives rise to complex dynamics as some parameters of the model are varied. Numerical simulations were used to show bifurcation diagram, stability region and chaos. It is also shown that the state variables feedback and parameter variation method can be used to keep the system from instability and chaos.