Abstract
We study the effect of decoherence on quantum Monty Hall problem under the influence of amplitude damping, depolarizing, and dephasing channels. It is shown that under the effect of decoherence, there is a Nash equilibrium of the game in case of depolarizing channel for Alice's quantum strategy. Whereas in case of dephasing noise, the game is not influenced by the quantum channel. For amplitude damping channel, Bob's payoffs are found symmetrical about a decoherence of 50% and the maximum occurs at this value of decoherence for his classical strategy. However, it is worth-mentioning that in case of depolarizing channel, Bob's classical strategy remains always dominant against any choice of Alice's strategy.