On the Efficiency of Nash Equilibria in the Interference Channel with Noisy Feedback

In this paper, the price of anarchy (PoA) and the price of stability (PoS) of the η-Nash equilibrium (η-NE), of the two-user linear deterministic interference channel with noisy channel-output feedback are characterized, with η > 0 arbitrarily small. The price of anarchy is the ratio between the sum-rate capacity and the smallest sum-rate at an η-NE. The price of stability is the ratio between the sum-rate capacity and the biggest sum-rate at an η-NE. Some of the main conclusions of this work are the following: (a) When both transmitter-receiver pairs are in low interference regime, the PoA can be made arbitrarily close to one as η approaches zero, subject to a particular condition. More specifically, there are scenarios in which even the worst η-NE (in terms of sum-rate) is arbitrarily close to the Pareto boundary of the capacity region. (b) The use of feedback plays a fundamental role on increasing the PoA, in some interference regimes. This is basically because in these regimes, the use of feedback increases the sum-capacity, whereas the smallest sum-rate at an η-NE remains the same. (c) The PoS is equal to one in all interference regimes. This implies that there always exists an η-NE in the Pareto boundary of the capacity region. The ensemble of conclusions of this work reveal the relevance of jointly using equilibrium selection methods and channel-output feedback for reducing the effect of anarchical behavior of the network components in the η-NE sum-rate of the interference channel.