Max-Min Fair Sensor Scheduling: Game-theoretic Perspective and Algorithmic Solution

TL;DR

This paper introduces a game-theoretic approach to designing max-min fair sensor schedules for monitoring multiple processes, ensuring equitable estimation error distribution across sensors.

Contribution

It reformulates the sensor scheduling problem as a zero-sum game and provides an algorithm to find the unique Nash equilibrium for fair resource allocation.

Findings

Existence of a unique Nash equilibrium in pure strategies.

Development of an equilibrium seeking procedure.

Application of the game-theoretic model to sensor scheduling.

Abstract

We consider the design of a fair sensor schedule for a number of sensors monitoring different linear time-invariant processes. The largest average remote estimation error among all processes is to be minimized. We first consider a general setup for the max-min fair allocation problem. By reformulating the problem as its equivalent form, we transform the fair resource allocation problem into a zero-sum game between a "judge" and a resource allocator. We propose an equilibrium seeking procedure and show that there exists a unique Nash equilibrium in pure strategy for this game. We then apply the result to the sensor scheduling problem and show that the max-min fair sensor scheduling policy can be achieved.