In this research report, the $\eta$-Nash equilibrium ($\eta$-NE) region of the two-user linear deterministic interference channel with noisy channel-output feedback is characterized for all $\eta > 0$ arbitrarily small. It also characterizes the $\eta$-Nash achievable region of the two-user Gaussian interference with noisy channel output feedback for all $\eta > 1$. The $\eta$-NE region, a subset of the capacity region, contains the set of all achievable information rate pairs that are stable in the sense of an $\eta$-NE. More specifically, given an $\eta$-NE coding scheme, there does not exist an alternative coding scheme for either transmitter-receiver pair that increases the individual rate by more than $\eta$ bits per channel use. Existing results such as the $\eta$-NE region of the linear deterministic interference channel and the Gaussian interference channel without feedback and with perfect output feedback are obtained as particular cases of the result presented in this research report.