"To sense" or "not to sense" in energy-efficient power control games

TL;DR

This paper analyzes a hierarchical game model for cognitive transmitters deciding on sensing and power control, revealing that joint decision-making can lead to worse outcomes than sequential strategies, highlighting a Braess-type paradox.

Contribution

It introduces a hybrid game framework combining sensing and power control decisions, showing the potential for suboptimal outcomes in joint strategies.

Findings

Sensing game is a weighted potential game.

Correlated equilibria are characterized.

Joint sensing and power control can be worse than sequential play.

Abstract

A network of cognitive transmitters is considered. Each transmitter has to decide his power control policy in order to maximize energy-efficiency of his transmission. For this, a transmitter has two actions to take. He has to decide whether to sense the power levels of the others or not (which corresponds to a finite sensing game), and to choose his transmit power level for each block (which corresponds to a compact power control game). The sensing game is shown to be a weighted potential game and its set of correlated equilibria is studied. Interestingly, it is shown that the general hybrid game where each transmitter can jointly choose the hybrid pair of actions (to sense or not to sense, transmit power level) leads to an outcome which is worse than the one obtained by playing the sensing game first, and then playing the power control game. This is an interesting Braess-type paradox to be aware of for energy-efficient power control in cognitive networks.