The Dynamics of Nash Equilibrium under Non-Markovian Classical Noise in Quantum Prisoners' Dilemma

The dynamics of the players' payoffs in the presence of non-Markovian classical static noise of quantum Prisoners' Dilemma is investigated. For a separable initial state, due to non-Markovianity of the environment, the prominence of the Nash equilibrium damps with the increasing coupling strength, and it completely disappears in the strong coupling limit. A similar behaviour is observed for initial entangled state against the time of interaction between the system and environment. A critical time of interaction exists beyond which the classical moves can perform better than any quantum move. For long time exposure, the memory effects of the environment dominate the strategies of the players, ending the game with a fixed payoff regardless of the players' moves.