Quantum Stackelberg duopoly in the presence of correlated noise

We study the influence of entanglement and correlated noise using correlated amplitude damping, depolarizing and phase damping channels on the quantum Stackelberg duopoly. Our investigations show that under the influence of an amplitude damping channel a critical point exists for an unentangled initial state at which firms get equal payoffs. The game becomes a follower advantage game when the channel is highly decohered. Two critical points corresponding to two values of the entanglement angle are found in the presence of correlated noise. Within the range of these limits of the entanglement angle, the game is a follower advantage game. In the case of a depolarizing channel, the payoffs of the two firms are strongly influenced by the memory parameter. The presence of quantum memory ensures the existence of the Nash equilibrium for the entire range of decoherence and entanglement parameters for both the channels. A local maximum in the payoffs is observed which vanishes as the channel correlation increases. Moreover, under the influence of the depolarizing channel, the game is always a leader advantage game. Furthermore, it is seen that the phase damping channel does not affect the outcome of the game.