A Game Theoretic Model for the Gaussian Broadcast Channel

TL;DR

This paper models the Gaussian broadcast channel as a generalized Nash equilibrium problem with coupled constraints, analyzing the strategic behavior of receivers using game theory and establishing conditions for equilibrium existence and uniqueness.

Contribution

It introduces a novel game-theoretic framework for the Gaussian broadcast channel with coupled strategies, using normalized equilibrium to analyze receiver behavior.

Findings

Existence of normalized equilibrium is proven for key scenarios.

Uniqueness of the equilibrium is established under certain conditions.

The model captures the strategic interaction of selfish receivers in the broadcast channel.

Abstract

The behavior of rational and selfish players (receivers) over a multiple-input multiple-output Gaussian broadcast channel is investigated using the framework of noncooperative game theory. In contrast to the game-theoretic model of the Gaussian multiple access channel where the set of feasible actions for each player is independent of other players' actions, the strategies of the players in the broadcast channel are mutually coupled, usually by a sum power or joint covariance constraint, and hence cannot be treated using traditional Nash equilibrium solution concepts. To characterize the strategic behavior of receivers connected to a single transmitter, this paper models the broadcast channel as a generalized Nash equilibrium problem with coupled constraints. The concept of normalized equilibrium (NoE) is used to characterize the equilibrium points and the existence and uniqueness of the NoE are proven for key scenarios.