Cost-sharing scheduling games on restricted unrelated machines

Guy Avni, Tami Tamir

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We study a very general cost-sharing scheduling game. An instance consists of k jobs and m machines and an arbitrary weighed bipartite graph denoting the job strategies. An edge connecting a job and a machine specifies that the job may choose the machine; edge weights correspond to processing times. Each machine has an activation cost that needs to be covered by the job assigned to it. Jobs assigned to a particular machine share its cost proportionally to the load they generate. Our game generalizes singleton cost-sharing games with weighted players. We provide a complete analysis of the game with respect to equilibrium existence, computation, convergence and quality – with respect to the total cost. We study both unilateral and coordinated deviations. We show that the main factor in determining the stability of an instance and the quality of a stable assignment is the machines’ activation-cost. Games with unit-cost machines are potential games, and every instance has an optimal solution which is also a pure Nash equilibrium (PNE). On the other hand, with arbitrary-cost machines, a PNE is guaranteed to exist only for very limited instances, and the price of stability is linear in the number of players. Also, the problem of deciding whether a given game instance has a PNE is NP-complete. In our analysis of coordinated deviations, we characterize instances for which a strong equilibrium exists and can be calculated efficiently, and show tight bounds for the SPoS and the SPoA.

Original languageEnglish
Title of host publicationAlgorithmic Game Theory - 8th International Symposium, SAGT 2015
EditorsMartin Hoefer, Martin Hoefer
PublisherSpringer Verlag
Number of pages13
ISBN (Print)9783662484326
StatePublished - 2015
Externally publishedYes
Event8th International Symposium on Algorithmic Game Theory, SAGT 2015 - Saarbrucken, Germany
Duration: 28 Sep 201530 Sep 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference8th International Symposium on Algorithmic Game Theory, SAGT 2015

Bibliographical note

Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2015.

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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