Two-qubit entangling operators as chaos control in a discrete dynamic Cournot duopoly game

The current trend in economics research is to incorporate quantum mechanical concepts to increase the security of business models. This interdisciplinary field of study represents real-world market dynamics more closely than do its classical counterparts. In this paper, we shed light on the significance of the two-qubit entangling operators in controlling chaos. We introduce a modified Eisert-Wilkens-Lewenstein scheme in a nonlinear Cournot duopoly game with complete and incomplete information. By doing so, the following interesting results are obtained: To begin, monopoly in a duopoly game can be avoided with the use of special perfect entanglers. Also, the stability analysis shows that there exists a class of entangling operators which can stabilize an unstable system and vice versa. Second, numerical analysis highlights the two-qubit entangling operators which can stabilize a chaotic system or at least delay chaos. Finally, we show that with an appropriate choice of initial state and speed of adjustments, entangling operators can decrease the sensitivity of the system. In short, while we know the importance of entangling operators in quantum game theory, in this paper we indicate the significance of operators in the context of a chaotic system.