The influence of entanglement on complex dynamics of a quantum Stackelberg duopoly with heterogeneous expectations

This paper investigates the complex dynamics of a nonlinear discrete-time Stackelberg duopoly game model by applying quantum game theory, where the players have heterogeneous expectations: the leader is boundedly rational and the follower thinks with adaptive expectation. The local stability of quantum equilibrium, the influence of quantum entanglement on stability region and complex dynamic behavior of the system are analyzed. The result shows that the stability of quantum Nash equilibrium can increase with the quantum entanglement increasing. The complex chaotic behaviors can appear when the quantum quantity adjustment speeds of bounded rational leader increase to a critical value, and a larger quantum entanglement will enhance the stability of the quantum Stackelberg duopoly system. Numerical simulations demonstrate the complex dynamic features via bifurcation, largest Lyapunov exponent, fractal dimensions, strange attractors and sensitivity to initial conditions.