Asymptotically Optimal Distributed Channel Allocation: a Competitive Game-Theoretic Approach

TL;DR

This paper introduces a novel game-theoretic approach to distributed channel allocation in large networks, ensuring near-optimal performance with high probability through a specially designed interference game and a distributed learning algorithm.

Contribution

It proposes the M-FSIG, a new non-cooperative game that guarantees convergence to optimal equilibria, and develops a distributed fictitious play algorithm for practical implementation.

Findings

Pure Nash equilibria are abundant and optimal in the proposed game.

The pure price of anarchy approaches one, indicating near-optimal efficiency.

The distributed algorithm converges quickly to the equilibria.

Abstract

In this paper 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. First we present a natural non-cooperative game theoretic formulation for this problem. It is shown that, when interference is sufficiently strong, this game has a pure price of anarchy approaching infinity with high probability, and there is an asymptotically increasing number of equilibria with the worst performance. Then we propose a novel non-cooperative M Frequency-Selective Interference Game (M-FSIG), where users limit their utility such that it is greater than zero only for their M best channels, and equal for them. We show that the M-FSIG exhibits, with high probability, an increasing number of optimal pure Nash equilibria and no bad equilibria. Consequently, the pure price of anarchy converges to one in probability in any interference regime. In order to exploit these results algorithmically we propose a modified Fictitious Play algorithm that can be implemented distributedly. We carry out simulations that show its fast convergence to the proven pure Nash equilibria.