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On the price of anarchy of two-stage machine scheduling games

Author

Listed:
  • Deshi Ye

    (Zhejiang University)

  • Lin Chen

    (Texas Tech University)

  • Guochuan Zhang

    (Zhejiang University)

Abstract

We consider a scheduling game, in which both the machines and the jobs are players. Machines are controlled by different selfish agents and attempt to maximize their workloads by choosing a scheduling policy among the given set of policies, while each job is controlled by a selfish agent that attempts to minimize its completion time by selecting a machine. Namely, this game was done in two-stage. In the first stage, every machine simultaneously chooses a policy from some given set of policies, and in the second stage, every job simultaneously chooses a machine. In this work, we use the price of anarchy to measure the efficiency of such equilibria where each machine is allowed to use one of the at most two policies. We provide nearly tight bounds for every combination of two deterministic scheduling policies with respect to two social objectives: minimizing the maximum job completion, and maximizing the minimum machine completion time.

Suggested Citation

  • Deshi Ye & Lin Chen & Guochuan Zhang, 2021. "On the price of anarchy of two-stage machine scheduling games," Journal of Combinatorial Optimization, Springer, vol. 42(3), pages 616-635, October.
    • Handle: RePEc:spr:jcomop:v:42:y:2021:i:3:d:10.1007_s10878-019-00474-2
    DOI: 10.1007/s10878-019-00474-2
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    References listed on IDEAS

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    1. Leah Epstein & Elena Kleiman & Rob Stee, 2014. "The cost of selfishness for maximizing the minimum load on uniformly related machines," Journal of Combinatorial Optimization, Springer, vol. 27(4), pages 767-777, May.
    2. Roughgarden, Tim & Tardos, Eva, 2004. "Bounding the inefficiency of equilibria in nonatomic congestion games," Games and Economic Behavior, Elsevier, vol. 47(2), pages 389-403, May.
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