In this paper, an achievable $η$-Nash equilibrium ($η$-NE) region for the two-user Gaussian interference channel with noisy channel-output feedback is presented for all $η\geqslant 1$. This result is obtained in the scenario in which each transmitter-receiver pair chooses its own transmit-receive configuration in order to maximize its own individual information transmission rate. At an $η$-NE, any unilateral deviation by either of the pairs does not increase the corresponding individual rate by more than $η$ bits per channel use.