Payoffs and coherence of a quantum two-player game under noisy environment

In this work, we mainly analyse the dynamics of quantum coherence, entanglement, geometric quantum discord and payoffs of a two-player quantum game under noisy environment. Our results indicate that unitary strategies do not change resource measures but change players' payoffs, and entangled operator changes both. Different measures have different variations with noise parameter and entanglement parameter. The behaviors of all quantifiers and payoffs in Markovian regime are different from the case of the non-Markovian regime. The case when only one of the two players is affected by noise gives different results from the case when the noise acts on both players. We find that the game symmetry is broken under noisy environment.