  We analyze quantum game with correlated noise through generalized
quantization scheme. Four different combinations on the basis of entanglement
of initial quantum state and the measurement basis are analyzed. It is shown
that the advantage that a quantum player can get by exploiting quantum
strategies is only valid when both the initial quantum state and the
measurement basis are in entangled form. Furthermore, it is shown that for
maximum correlation the effects of decoherence diminish and it behaves as a
noiseless game.
