  We reformulate the quantum Monty Hall problem in the presence of decoherence.
The decoherence destroys the fairness of the game. A new Nash equilibrium for a
particular strategy profile in the presence of decoherence emerges. It is shown
that in the presence of decoherence under the action of amplitude damping
channel, Bob's winning probability is always higher than three-forth,
irrespective of Alice's strategy, if he does not switch to the other door and
always wins for a fully decohered case of the channel. Depolarizing channel
damps up Bob's winning probability and gets better off if he sticks to his
current selection. Phase damping channel leaves the winning probability
unaffected. Unlike the classical and the quantum forms of the game, Bob's
dominant strategy in the presence of decoherence is not switching.
