The Gaussian Multiple Access Wiretap Channel with Selfish Transmitters: A Coalitional Game Theory Perspective

TL;DR

This paper investigates how selfish transmitters in a Gaussian multiple access wiretap channel can benefit from cooperation, using coalitional game theory to identify stable, fair protocols that maximize individual secrecy rates.

Contribution

It applies coalitional game theory to analyze cooperation incentives among selfish transmitters in GMAC-WT, establishing the existence of stable, fair secrecy rate allocations.

Findings

Cooperation benefits all transmitters in degraded GMAC-WT.

Stable, fair secrecy rate allocations are achievable.

In non-degraded GMAC-WT, cooperation depends on channel parameters.

Abstract

This paper considers the Gaussian multiple access wiretap channel (GMAC-WT) with selfish transmitters, i.e., who are each solely interested in maximizing their individual secrecy rate. The question then arises as to whether selfish transmitters can increase their individual secrecy rate by participating in a collective, i.e., multiple access, protocol instead of operating on their own. If yes, the question arises whether there is a protocol that satisfies all the participating transmitters simultaneously, in the sense that no transmitter has an incentive to deviate from the protocol. Utilizing coalitional game theory, these questions are addressed for the degraded GMAC-WT with an arbitrary number of transmitters and for the non-degraded GMAC-WT with two transmitters. In particular, for the degraded GMAC-WT, cooperation is shown to be in the best interest of all transmitters, and the existence of protocols that incentivize all transmitters to participate is established. Furthermore, a unique, fair, stable, and achievable secrecy rate allocation is determined. For the non-degraded GMAC-WT, depending on the channel parameters, there are cases where cooperation is not in the best interest of all transmitters, and cases where it is. In the latter cases, a unique, fair, stable, and achievable secrecy rate allocation is determined.