Extending the bargain region using beamforming design under mixed QoS constraints

In this work, we demonstrate how the bargain region can be extended by using mixed quality-of-service (QoS) optimization in a two-user game. We show that the bargain region extension is linked with a new Nash equilibrium (NE) point, which we call the NE-mixed QoS. We studied the performance of two systems from game-theoretic perspective. The first one considered a situation where both players want to maximize their utilities and therefore it will always use the unscaled maximum ratio transmission (MRT) beamformers to reach the NE. We considered a second system which uses mixed QoS criterion to form a game where one player wants to maximize its utility while the other player wants to minimize its cost function. We show that the second system is able to achieve high average sum rates while consuming less power as compared to the first system.