On the Nash Equilibria in Decentralized Parallel Interference Channels

TL;DR

This paper models a decentralized interference channel as a non-cooperative game, analyzing the existence and number of Nash equilibria in power allocation and channel selection scenarios, with implications for spectral efficiency.

Contribution

It provides a novel analysis of Nash equilibria in decentralized interference channels, including existence, multiplicity, and spectral efficiency comparisons between strategies.

Findings

Multiple Nash equilibria can occur in both game scenarios.

Spectral efficiency at NE is higher in channel selection than in power allocation.

Monte-Carlo simulations confirm the efficiency advantages of channel selection.

Abstract

In this paper, the 2-dimensional decentralized parallel interference channel (IC) with 2 transmitter-receiver pairs is modelled as a non-cooperative static game. Each transmitter is assumed to be a fully rational entity with complete information on the game, aiming to maximize its own individual spectral efficiency by tuning its own power allocation (PA) vector. Two scenarios are analysed. First, we consider that transmitters can split their transmit power between both dimensions (PA game). Second, we consider that each transmitter is limited to use only one dimension (channel selection CS game). In the first scenario, the game might have either one or three NE in pure strategies (PS). However, two or infinitely many NE in PS might also be observed with zero probability. In the second scenario, there always exists either one or two NE in PS. We show that in both games there always exists a non-zero probability of observing more than one NE. More interestingly, using Monte-Carlo simulations, we show that the highest and lowest network spectral efficiency at any of the NE in the CS game are always higher than the ones in the PA.