We investigate a scenario where two transmitters, Alice and Bob, send information to a passive receiver, Charlie through a quantum channel. We use a method based on quantum entanglement and apply game theory. In this setup, Alice and Bob each have a chance of successfully sending their messages and being entanglement with probability p and q, respectively, and there is a cost c involved. Our main focus is on using entanglement to assess the Price of Anarchy (PoA), which measures the degradation induced by selfish behavior when multiple players are involved. The most important result of our analysis is that the Price of Anarchy becomes very high when there are multiple Nash equilibria. This means that these systems require a careful management to avoid bad outcomes. Thus, we propose an implementable schematic (a network architecture based on entangled photons) to demonstrate how the game can be utilized in a real 5G network.