Decentralized interference channels with noisy feedback possess Pareto optimal Nash equilibria

In this paper, the price of anarchy (PoA) and the price of stability (PoS) of a game arising in a two-user decentralized interference channel (DIC) with noisy feedback in which transmit-receiver pairs seek an optimal individual transmission rate are fully characterized. In particular, it is shown that in all interference regimes, there always exists at least one Pareto optimal Nash equilibrium (NE). More specifically, there always exists an NE at which players maximize the network sum-rate and thus, the PoS of the corresponding game is always equal to one. A second result provides closed form expressions for the PoA, which allows the full characterization of the reduction of the sum rate due to the anarchic behavior of all transmitter-receiver pairs.