# Game Theoretic Dynamic Channel Allocation for Frequency-Selective Interference Channels

## TL;DR

This paper introduces a distributed game-theoretic algorithm for channel allocation in frequency-selective interference channels, ensuring near-optimal performance at equilibrium without requiring user communication.

## Contribution

It proposes a novel utility design within a non-cooperative game that guarantees asymptotically optimal equilibria in large interference networks.

## Key findings

- Algorithm converges quickly to optimal equilibria.
- Even worst-case equilibria achieve near-optimal sum-rate.
- Analysis applies to various fading channel distributions.

## Abstract

We consider the problem of distributed channel allocation in large networks under the frequency-selective interference channel. Performance is measured by the weighted sum of achievable rates. Our proposed algorithm is a modified Fictitious Play algorithm that can be implemented distributedly and its stable points are the pure Nash equilibria of a given game. Our goal is to design a utility function for a non-cooperative game such that all of its pure Nash equilibria have close to optimal global performance. This will make the algorithm close to optimal while requiring no communication between users. We propose a novel technique to analyze the Nash equilibria of a random interference game, determined by the random channel gains. Our analysis is asymptotic in the number of users. First we present a natural non-cooperative game where the utility of each user is his achievable rate. It is shown that, asymptotically in the number of users and for strong enough interference, this game exhibits many bad equilibria. Then we propose a novel non-cooperative M Frequency-Selective Interference Channel Game (M-FSIG), as a slight modification of the former, where the utility of each user is artificially limited. We prove that even its worst equilibrium has asymptotically optimal weighted sum-rate for any interference regime and even for correlated channels. This is based on an order statistics analysis of the fading channels that is valid for a broad class of fading distributions (including Rayleigh, Rician, m-Nakagami and more). We carry out simulations that show fast convergence of our algorithm to the proven asymptotically optimal pure Nash equilibria.