In this paper, the η-Nash equilibrium (η-NE) region of the two-user Gaussian interference channel (IC) with perfect output feedback is approximated to within 1 bit/s/Hz and η arbitrarily close to 1 bit/s/Hz. The relevance of the η-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 η-optimal individual transmission rate. Therefore, any rate tuple outside the η-NE region is not stable as there always exists one link able to increase by at least η bits/s/Hz its own transmission rate by updating its own transmit-receive configuration. The main insights that arise from this paper are as follows. First, the η-NE region achieved with feedback is larger than or equal to the η-NE region without feedback. More importantly, for each rate pair achievable at an η-NE without feedback, there exists at least one rate pair achievable at an η-NE with feedback that is weakly Pareto superior. Second, there always exists an η-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.