The influence of entanglement and decoherence on the quantum Stackelberg duopoly game

In this paper, we investigate the influence of entanglement and decoherence on the quantum Stackelberg duopoly ( QSD) game. It is shown that the first- mover advantage can be weakened or enhanced due to the existence of entanglement for the QSD game without decoherence. The influence of decoherence induced by the amplitude damping and the phase damping are explicitly studied in the formalism of Kraus operator representations. We show that the amplitude damping drastically changes the Nash equilibrium of the QSD game and the profits of the two players while the phase damping does not affect the Nash equilibrium and the profits of the two players. It is found that under certain conditions there exists a 'critical point' of the damping parameter for the amplitude damping environment. At the ` critical point' the two players have the same moves and payoffs. The QSD game can change from the first- mover advantage game into the follower- mover advantage game when the damping parameter varies from the left- hand- side regime of the ` critical point' to the right- hand- side regime.