Abstract
In this paper, we investigate the quantum Stackelberg duopoly (QSD) game in the noise environment with the depolarizing channel expressed by the Kraus-operator representation. It is found that the presence of the damping in the depolarizing channel always leads to the decrease of the quantities of the moves and payoffs of the two players in the QSD game. It is indicated that under certain conditions the first-mover advantage in the QSD game can be weakened due to the presence of the damping in the depolarizing channel.