  The influence of noise and of Unruh effect on quantum Prisoners' dilemma is
investigated both for entangled and unentangled initial states. The noise is
incorporated through amplitude damping channel. For unentangled initial state,
the decoherence compensates for the adverse effect of acceleration of the frame
and the effect of acceleration becomes irrelevant provided the game is fully
decohered. It is shown that the inertial player always out scores the
noninertial player by choosing defection. For maximally entangled initially
state, we show that for fully decohered case every strategy profile results in
either of the two possible equilibrium outcomes. Two of the four possible
strategy profiles become Pareto Optimal and Nash equilibrium and no dilemma is
leftover. It is shown that other equilibrium points emerge for different region
of values of decoherence parameter that are either Pareto optimal or Pareto
inefficient in the quantum strategic spaces. It is shown that the Eisert et al
miracle move is a special move that leads always to distinguishable results
compare to other moves. We show that the dilemma like situation is resolved in
favor of one player or the other.
