A New Perspective on Multi-user Power Control Games in Interference Channels

TL;DR

This paper introduces a Stackelberg game framework for multi-user power control in interference channels, showing foresighted users can outperform myopic strategies when they have sufficient channel information.

Contribution

It models a foresighted user in interference channels using Stackelberg equilibrium, providing analytical insights and a low-complexity solution for strategic power control.

Findings

Foresighted users can improve performance with knowledge of competitors' strategies.

The Stackelberg equilibrium exists for the non-cooperative game.

A practical low-complexity approach based on Lagrangian duality is proposed.

Abstract

This paper considers the problem of how to allocate power among competing users sharing a frequency-selective interference channel. We model the interaction between selfish users as a non-cooperative game. As opposed to the existing iterative water-filling algorithm that studies the myopic users, this paper studies how a foresighted user, who knows the channel state information and response strategies of its competing users, should optimize its transmission strategy. To characterize this multi-user interaction, the Stackelberg equilibrium is introduced, and the existence of this equilibrium for the investigated non-cooperative game is shown. We analyze this interaction in more detail using a simple two-user example, where the foresighted user determines its transmission strategy by solving as a bi-level program which allows him to account for the myopic user's response. It is analytically shown that a foresighted user can improve its performance, if it has the necessary information about its competitors. Since the optimal solution of Stackelberg equilibrium is computationally prohibitive, we propose a practical low-complexity approach based on Lagrangian duality theory. Numerical simulations verify the performance improvements. Possible ways to acquire the required information and to extend the formulation to more than two users are also discussed.