Cost-sharing scheduling games on restricted unrelated machines

Guy Avni, Tami Tamir

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

Abstract

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 languageAmerican English
Title of host publicationAlgorithmic Game Theory - 8th International Symposium, SAGT 2015
EditorsMartin Hoefer
PublisherSpringer Verlag
Pages69-81
Number of pages13
ISBN (Print)9783662484326
DOIs
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)
Volume9347

Conference

Conference8th International Symposium on Algorithmic Game Theory, SAGT 2015
Country/TerritoryGermany
CitySaarbrucken
Period28/09/1530/09/15

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science

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