Scheduling games with machine-dependent priority lists

Vipin Ravindran Vijayalakshmi, Marc Schröder, Tami Tamir*

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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Abstract

We consider a scheduling game on parallel related machines, in which jobs try to minimize their completion time by choosing a machine to be processed on. Each machine uses an individual priority list to decide on the order according to which the jobs on the machine are processed. We prove that it is NP-hard to decide if a pure Nash equilibrium exists and characterize four classes of instances in which a pure Nash equilibrium is guaranteed to exist. For each of these classes, we give an algorithm that computes a Nash equilibrium, we prove that best-response dynamics converge to a Nash equilibrium, and we bound the inefficiency of Nash equilibria with respect to the makespan of the schedule and the sum of completion times. In addition, we show that although a pure Nash equilibrium is guaranteed to exist in instances with identical machines, it is NP-hard to approximate the best Nash equilibrium with respect to both objectives. (C) 2020 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)90-103
Number of pages14
JournalTheoretical Computer Science
Volume855
Early online date1 Dec 2020
DOIs
Publication statusPublished - 6 Feb 2021

Keywords

  • equilibrium inefficiency
  • priority lists
  • scheduling games
  • Equilibrium inefficiency
  • DESIGN
  • EQUILIBRIA
  • PRICE
  • Priority lists
  • BOUNDS
  • Scheduling games
  • COORDINATION MECHANISMS
  • CONGESTION GAMES

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