Noisy non-transitive quantum games

We study the effect of quantum noise in 3 by 3 entangled quantum games. By considering different noisy quantum channels we analyze that how a two-player, three-strategy Rock-Scissor-Paper game is influenced by the quantum noise. We consider the winning non-transitive strategies R, S and P such as R beats S, S beats P, and P beats R. The game behaves as a noiseless game for maximum value of the quantum noise parameter. It is seen that Alice's payoff is heavily influenced by the depolarizing noise as compared to the amplitude damping noise. Depolarizing channel causes a monotonic decrease in players payoffs as we increase the amount of of quantum noise. In case of amplitude damping channel, the Alice's payoff function reaches its minimum for alpha=0.5 and is symmetrical. This means that larger values of quantum noise influence the game weakly. On the other hand, phase damping channel does not influence the game's payoff. Furthermore, the game's Nash equilibrium and non-transitive character of the game are not affected under the influence of quantum noise.