Complex dynamics and chaos control of a quantum Stackelberg game with heterogeneous players

Abstract

In this research article, we explore the complex dynamics of a quantum Stackelberg game and its chaos control involving players with heterogeneous expectations. We utilize the Iqbal & Toor scheme to quantize the classical Stackelberg game and observe that the first mover advantage is diminished in the quantum version of the game. By examining the game from an evolutionary perspective, where the leader firm employs bounded rational expectations and the follower firm adopts adaptive expectations, we discover that the quantum Stackelberg game exhibits complex behaviors, such as cyclic and chaotic states. The local stability of the quantum game depends on the initial state of the game. Additionally, the occurrence of chaos is delayed in the quantum game. To further investigate, we implement the time-delayed feedback method to control the chaos in the quantum game and demonstrate that the techniques used for controlling the classical game are still effective in the quantum game.