  This paper considers the competitive resource allocation problem in
Multiple-Input Multiple-Output (MIMO) interfering channels, when users maximize
their energy efficiency. Considering each transmitter-receiver pair as a
selfish player, conditions on the existence and uniqueness of the Nash
equilibrium of the underlying noncooperative game are obtained. A decentralized
asynchronous algorithm is proven to converge towards this equilibrium under the
same conditions. Two frameworks are considered for the analysis of this game.
On the one hand, the game is rephrased as a Quasi-Variational Inequality (QVI).
On the other hand, the best response of the players is analyzed in light of the
contraction mappings. For this problem, the contraction approach is shown to
lead to tighter results than the QVI one. When specializing the obtained
results to OFDM networks, the obtained conditions appear to significantly
outperform state-of-the-art works, and to lead to much simpler decentralized
algorithms. Numerical results finally assess the obtained conditions in
different settings.
