Interval Scheduling Games

Vipin Ravindran Vijayalakshmi

doi:10.1007/978-3-032-12915-4_8

Return

Interval Scheduling Games

2026-01-01

PRE

Vipin Ravindran Vijayalakshmi

Marc Schröder

Tami Tamir *

DOI：10.1007/978-3-032-12915-4_8

Original

Save

Abstract

En 中文

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.

Keywords:

Interval scheduling

Scheduling games

Equilibrium inefficiency