Chaotic dynamics in differentiated Bertrand model with heterogeneous players

A nonlinear differentiated Bertrand duopoly game is investigated comprehensively, where players have heterogeneous expectations and nonlinear cost function. Two types of players are considered including both bounded rational and naive expectation types. The equilibrium point and local stability of the duopoly game are studied in details. It is demonstrated that as some parameters of the game are varied, the stability of Nash equilibrium is broken during the period of doubling bifurcation. The chaotic features are justified numerically via computing Lyapunov exponents and sensitive dependence on initial conditions.