Interval Scheduling Games

TL;DR

This paper studies a game-theoretic variant of interval scheduling where players control jobs of different colors, analyzing equilibrium existence, computation, and efficiency, with applications like wireless antenna scheduling.

Contribution

It introduces a new game-theoretic model for interval scheduling with multiple players and analyzes Nash equilibria and their properties, extending classical scheduling theory.

Findings

Polynomial-time solution for fixed strategy profiles.

Existence and computation of Nash equilibria analyzed.

Inefficiency of equilibria studied.

Abstract

We consider a game-theoretic variant of an interval scheduling problem. Every job is associated with a length, a weight, and a color. Each player controls all the jobs of a specific color, and needs to decide on a processing interval for each of its jobs. Jobs of the same color can be processed simultaneously by the machine. A job is covered if the machine is configured to its color during its whole processing interval. The goal of the machine is to maximize the sum of weights of all covered jobs, and the goal of each player is to place its jobs such that the sum of weights of covered jobs from its color is maximized. The study of this game is motivated by several applications like antenna scheduling for wireless networks. We first show that given a strategy profile of the players, the machine scheduling problem can be solved in polynomial time. We then study the game from the players' point of view. We analyze the existence of Nash equilibria, its computation, and inefficiency. We distinguish between instances of the classical interval scheduling problem, in which every player controls a single job, and instances in which color sets may include multiple jobs.