Global dynamics of a quantum Cournot duopoly with quadratic costs and relative profit maximization

Abstract

To be more realistic, this paper considers the pursuit of maximizing relative profits by firms, establishes a Cournot duopoly game model with quantum entanglement, and investigates how quantum entanglement influences decisions made by the firms. Following that, the Jacobi matrix and Jury criterion are used to examine the local stability of the Nash equilibrium. Additionally, the impact of various model parameters on system stability is investigated by implementing a numerical experiment. It has been found that limiting the adjustment speed and squeezing parameter to an appropriate range contributes to the long-term stability of the market. The coexistence of attractors is then fully investigated by means of the basin of attraction. The coexistence of attractors provides insights into the complexity and diversity of dynamic systems, shedding light on their nonlinear nature and sensitivity to initial conditions. Finally, the critical curve and the noninvertible map allow us to examine the global dynamics of the system.