Selfish Jobs with Favorite Machines: Price of Anarchy vs. Strong Price of Anarchy View Full Text


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Chapter Info

DATE

2017-11-16

AUTHORS

Cong Chen , Paolo Penna , Yinfeng Xu

ABSTRACT

We consider the well-studied game-theoretic version of machine scheduling in which jobs correspond to self-interested users and machines correspond to resources. Here each user chooses a machine trying to minimize her own cost, and such selfish behavior typically results in some equilibrium which is not globally optimal: An equilibrium is an allocation where no user can reduce her own cost by moving to another machine, which in general need not minimize the makespan, i.e., the maximum load over the machines. We provide tight bounds on two well-studied notions in algorithmic game theory, namely, the price of anarchy and the strong price of anarchy on machine scheduling setting which lies in between the related and the unrelated machine case. Both notions study the social cost (makespan) of the worst equilibrium compared to the optimum, with the strong price of anarchy restricting to a stronger form of equilibria. Our results extend a prior study comparing the price of anarchy to the strong price of anarchy for two related machines (Epstein [13], Acta Informatica 2010), thus providing further insights on the relation between these concepts. Our exact bounds give a qualitative and quantitative comparison between the two models. The bounds also show that the setting is indeed easier than the two unrelated machines: In the latter, the strong price of anarchy is 2, while in ours it is strictly smaller. More... »

PAGES

226-240

References to SciGraph publications

  • 2015-10. Mechanisms for Scheduling with Single-Bit Private Values in THEORY OF COMPUTING SYSTEMS
  • 2009. Strong and Pareto Price of Anarchy in Congestion Games in AUTOMATA, LANGUAGES AND PROGRAMMING
  • 2008. The Price of Stochastic Anarchy in ALGORITHMIC GAME THEORY
  • 2015-01. Some Anomalies of Farsighted Strategic Behavior in THEORY OF COMPUTING SYSTEMS
  • 2003. Nashification and the Coordination Ratio for a Selfish Routing Game in AUTOMATA, LANGUAGES AND PROGRAMMING
  • 2010-12. Equilibria for two parallel links: the strong price of anarchy versus the price of anarchy in ACTA INFORMATICA
  • 2007. Strong Price of Anarchy for Machine Load Balancing in AUTOMATA, LANGUAGES AND PROGRAMMING
  • 2002-04-12. Worst-Case Equilibria in STACS 99
  • 1979-09. A linear time approximation algorithm for multiprocessor scheduling in BIT NUMERICAL MATHEMATICS
  • 2014. The Sequential Price of Anarchy for Atomic Congestion Games in WEB AND INTERNET ECONOMICS
  • 2003-12. Approximate Equilibria and Ball Fusion in THEORY OF COMPUTING SYSTEMS
  • Book

    TITLE

    Combinatorial Optimization and Applications

    ISBN

    978-3-319-71146-1
    978-3-319-71147-8

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/978-3-319-71147-8_16

    DOI

    http://dx.doi.org/10.1007/978-3-319-71147-8_16

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1092714467


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