Chaotic dynamics and chaos control in differentiated Bertrand model with heterogeneous players

Abstract

PurposeThe purpose of this paper is to investigate the chaotic dynamics behaviours and chaos control of differentiated Bertrand model.Design/methodology/approachThe paper analyzes a nonlinear differentiated Bertrand duopoly game by using the theory of bifurcations of dynamical system, where players have heterogeneous expectations and nonlinear cost function: two types of players are considered – bounded rational and naive expectation. The equilibrium point and local stability of the duopoly game are investigated.FindingsThe paper demonstrates that as some parameters of the game are varied, the stability of Nash equilibrium is lost through period doubling bifurcation. The chaotic features are justified numerically via computing Lyapunov exponents, and sensitive dependence on initial conditions. By using the delay feedback control method, the authors have made the system form chaotic state to stable state.Originality/valueThis paper fulfils an identified need to study the diversity of expectations and how to lead to rich dynamics and complexity.