关键词: Stackelberg duopoly game, memory effects, payoff, amplitude-damping channel

Abstract: We study the influence of memory effects on the quantum Stackelberg duopoly game through an amplitude-damping channel where successive uses of the channels are correlated. It is shown that the memory effects can drastically change the Nash equilibrium and the payoffs of the two firms. As the degree of channel memory increases, there exists a Nash equilibrium for the entire range of the entanglement parameter. Similarly, the presence of memory ensures the existence of the Nash equilibrium for the whole range of the decoherence parameter both for entangled and unentangled initial states. Moreover, quantum memory leads to a ‘critical point’ of the damping parameter, at which both firms are equally benefited. With the maximum-memory effect, the position of the ‘critical point’ moves to the place of fully decohered.

Key words: Stackelberg duopoly game, memory effects, payoff, amplitude-damping channel