Chaotic dynamics of a quantum Cournot duopoly game with heterogeneous expectations

Abstract

On the basis of the bounded rationality and adaptive expectations, we investigate the dynamics of quantum Cournot duopoly game with heterogeneous players by using the Li et al. scheme. Further, we discuss the effect of quantum entanglement on local stability of the system. The results show that: (i) The special form of quantum Cournot duopoly game is the classical Cournot duopoly game, and the quantum Cournot duopoly game with naïve expectation is also a special form of quantum Cournot duopoly game with adaptive expectation. (ii) The increase or decrease of the stable region is dependent on the degree of quantum entanglement. It is related to the difference of relative marginal cost. (iii) The numerical simulation reveals the complexity characteristics of quantum dynamic Cournot game system through the analysis of stability region, bifurcation, strange attractor and sensitivity to initial conditions, and shows the difference from the classical dynamic Cournot model.