Power Allocation Games in Interference Relay Channels: Existence Analysis of Nash Equilibria

TL;DR

This paper analyzes the existence, uniqueness, and efficiency of Nash equilibria in a multi-band interference relay channel game where two selfish transmitters allocate resources to maximize their individual rates, considering three relaying protocols.

Contribution

It provides the first comprehensive analysis of Nash equilibria existence and properties in interference relay channels with multiple relaying strategies.

Findings

Nash equilibria exist for decode-and-forward, estimate-and-forward, and amplify-and-forward protocols.

Conditions for the uniqueness and efficiency of equilibria are identified.

Simulations illustrate the convergence of best-response dynamics to equilibria.

Abstract

We consider a network composed of two interfering point-to-point links where the two transmitters can exploit one common relay node to improve their individual transmission rate. Communications are assumed to be multi-band and transmitters are assumed to selfishly allocate their resources to optimize their individual transmission rate. The main objective of this paper is to show that this conflicting situation (modeled by a non-cooperative game) has some stable outcomes, namely Nash equilibria. This result is proved for three different types of relaying protocols: decode-and-forward, estimate-and-forward, and amplify-and-forward. We provide additional results on the problems of uniqueness, efficiency of the equilibrium, and convergence of a best-response based dynamics to the equilibrium. These issues are analyzed in a special case of the amplify-and-forward protocol and illustrated by simulations in general.