  In this paper, the 2-dimensional decentralized parallel interference channel
(IC) with 2 transmitter-receiver pairs is modelled as a non-cooperative static
game. Each transmitter is assumed to be a fully rational entity with complete
information on the game, aiming to maximize its own individual spectral
efficiency by tuning its own power allocation (PA) vector. Two scenarios are
analysed. First, we consider that transmitters can split their transmit power
between both dimensions (PA game). Second, we consider that each transmitter is
limited to use only one dimension (channel selection CS game). In the first
scenario, the game might have either one or three NE in pure strategies (PS).
However, two or infinitely many NE in PS might also be observed with zero
probability. In the second scenario, there always exists either one or two NE
in PS. We show that in both games there always exists a non-zero probability of
observing more than one NE. More interestingly, using Monte-Carlo simulations,
we show that the highest and lowest network spectral efficiency at any of the
NE in the CS game are always higher than the ones in the PA.
