Nonlinear Dynamics of a Quantum Cournot Duopoly with Bounded Rationality and Relative Profit Maximization

Abstract

Based on boundary rationality and relative profit maximization, quantum game theory is applied to develop a dynamic model of the quantum Cournot duopoly game. We investigate the effect of quantum properties on game stability and nonlinear dynamics. The results show that quantum entanglement can improve the model’s stability and control the generation of bifurcation and chaos when comparing the classical game and the game without considering relative profit maximization. It facilitates the player’s choice of quantum entanglement to control the chaos that emerges in the production output. Numerical simulations verify the chaotic properties of the game by means of bifurcations, maximum Lyapunov exponents, and phase diagrams. The results show that quantum entanglement has different effects on different games.