  In this paper, the $\eta$-Nash equilibrium ($\eta$-NE) region of the two-user
Gaussian interference channel (IC) with perfect output feedback is approximated
to within $1$ bit/s/Hz and $\eta$ arbitrarily close to $1$ bit/s/Hz. The
relevance of the $\eta$-NE region is that it provides the set of rate-pairs
that are achievable and stable in the IC when both transmitter-receiver pairs
autonomously tune their own transmit-receive configurations seeking an
$\eta$-optimal individual transmission rate. Therefore, any rate tuple outside
the $\eta$-NE region is not stable as there always exists one link able to
increase by at least $\eta$ bits/s/Hz its own transmission rate by updating its
own transmit-receive configuration. The main insights that arise from this work
are: $(i)$ The $\eta$-NE region achieved with feedback is larger than or equal
to the $\eta$-NE region without feedback. More importantly, for each rate pair
achievable at an $\eta$-NE without feedback, there exists at least one rate
pair achievable at an $\eta$-NE with feedback that is weakly Pareto superior.
$(ii)$ There always exists an $\eta$-NE transmit-receive configuration that
achieves a rate pair that is at most $1$ bit/s/Hz per user away from the outer
bound of the capacity region.
