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

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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.

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Acknowledgements

The authors thank anonymous referees for helpful comments and suggestions to improve the presentation of this paper.

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Authors and Affiliations

  1. College of Computer Science, Zhejiang University, Hangzhou, 310027, China

    Deshi Ye & Guochuan Zhang

  2. Department of Computer Science, Texas Tech University, Lubbock, TX, USA

    Lin Chen

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  1. Deshi Ye
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  2. Lin Chen
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  3. Guochuan Zhang
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Correspondence to Deshi Ye.

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A preliminary version of this paper appeared in the 11th International Conference on Combinatorial Optimization and Applications (COCOA 2017,pp. 214–225). Research was supported in part by NSFC (11671355, 11771365) and NSF (1756014).

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Ye, D., Chen, L. & Zhang, G. On the price of anarchy of two-stage machine scheduling games. J Comb Optim 42, 616–635 (2021). https://doi.org/10.1007/s10878-019-00474-2

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