# Nash Region of the Linear Deterministic Interference Channel with Noisy Output Feedback

## TL;DR

This paper characterizes the $ ext{eta}$-Nash equilibrium region of the two-user linear deterministic interference channel with noisy output feedback, extending previous results to include noisy feedback scenarios.

## Contribution

It provides a comprehensive characterization of the $ ext{eta}$-NE region with noisy feedback, generalizing prior work with perfect or no feedback.

## Key findings

- The $ ext{eta}$-NE region is explicitly characterized for all $ ext{eta} > 0$.
- Existing results are recovered as special cases of the new characterization.
- The work extends understanding of stable rate pairs in interference channels with noisy feedback.

## Abstract

In this paper, the $\eta$-Nash equilibrium ($\eta$-NE) region of the two-user linear deterministic interference channel (IC) with noisy channel-output feedback is characterized for all $\eta > 0$. 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 IC without feedback and with perfect output feedback are obtained as particular cases of the result presented in this paper.