On the Existence and Structure of Mixed Nash Equilibria for In-Band Full-Duplex Wireless Networks

TL;DR

This paper characterizes the conditions for the existence of mixed Nash equilibria in full-duplex wireless networks sharing a channel, highlighting the importance of self-interference cancellation accuracy and cost proportionality.

Contribution

It provides the first analytical characterization of mixed Nash equilibria in full-duplex wireless systems with Aloha contention, linking equilibrium existence to cost proportionality.

Findings

Mixed Nash equilibria exist only with proportional costs related to self-interference cancellation.

Proper cost selection can lead to equilibria that optimize network throughput.

System performance is sensitive to cost parameters, affecting the price of anarchy.

Abstract

This article offers the first characterisation of mixed Nash equilibria (MNE) for a wireless system with full-duplex capable terminals that share a common channel via Aloha-based contention. Focussing on a simple grid topology, we prove that mixed MNE exist only if proportionality, driven by the accuracy of self-interference cancellation, is granted between the cost undergone for full- and half-duplex operations. The analysis shows how a proper selection of such costs allows MNE that are also optimal from a network viewpoint in terms of aggregate throughput. The sensitivity of system performance to costs is tackled and discussed considering the price of anarchy.