Quantum Stackelberg duopoly in the presence of correlated noise

TL;DR

This paper investigates how different types of correlated noise and entanglement affect the outcomes of a quantum Stackelberg duopoly, revealing critical points, the role of quantum memory, and the conditions for leader or follower advantage.

Contribution

It provides a detailed analysis of the effects of correlated amplitude damping, depolarizing, and phase damping channels on quantum duopoly outcomes, highlighting the impact of entanglement and quantum memory.

Findings

Amplitude damping causes a critical point with equal payoffs for unentangled states.

Depolarizing channel payoffs are strongly influenced by quantum memory.

Phase damping does not affect the game's outcome.

Abstract

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 action of amplitude damping channel a critical point exists for unentangled initial state as well, 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 entanglement angle, the game is follower advantage game. In case of depolarizing channel, the payoffs of the two firms are strongly influenced by the memory parameter. The presence of quantum memory ensures the existence of 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 depolarizing channel, the game is always a leader advantage game. Furthermore, it is seen that phase damping channel does not effect the outcome of the game.