Equilibria of Channel Selection Games in Parallel Multiple Access Channel

TL;DR

This paper analyzes the Nash equilibria in decentralized channel selection games for parallel MACs, revealing a paradox where more available channels can reduce overall spectral efficiency, and explores the impact of successive interference cancellation.

Contribution

It provides a mathematical proof of a Braess-type paradox in channel selection games and characterizes the NE structure in fully loaded networks.

Findings

Existence of at least one pure NE in the game.

In fully loaded networks, more channels can decrease spectral efficiency at NE.

Power allocation at NE maximizes capacity with successive interference cancellation.

Abstract

In this paper, we study the decentralized parallel multiple access channel (MAC) when transmitters selfishly maximize their individual spectral efficiency by selecting a single channel to transmit. More specifically, we investigate the set of Nash equilibria (NE) of decentralized networks comprising several transmitters communicating with a single receiver that implements single user decoding. This scenario is modeled as a one-shot game where the players (the transmitters) have discrete action sets (the channels). We show that the corresponding game has always at least one NE in pure strategies, but, depending on certain parameters, the game might possess several NE. We provide an upper bound for the maximum number of NE as a function of the number of transmitters and available channels. The main contribution of this paper is a mathematical proof of the existence of a Braess-type paradox. In particular, it is shown that under the assumption of a fully loaded network, when transmitters are allowed to use all the available channels, the corresponding sum spectral efficiency achieved at the NE is lower or equal than the sum spectral efficiency achieved when transmitters can use only one channel. A formal proof of this observation is provided in the case of small networks. For general scenarios, we provide numerical examples that show that the same effect holds as long as the network is kept fully loaded. We conclude the paper by considering the case of successive interference cancellation at the receiver. In this context, we show that the power allocation vectors at the NE are capacity maximizers. Finally, simulations are presented to verify our theoretical results.