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Improved price of anarchy for machine scheduling games with coordination mechanisms

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Abstract

We study several machine scheduling games, each involving n jobs to be processed on m uniformly related machines. Each job, as an agent, selects a machine for processing to minimize his disutility (e.g., the completion time of the agent). We analyze the price of anarchy (PoA) for these scheduling games, where the PoA is defined as maximum ratio of the central objective value of the worst pure Nash equilibrium over the optimal central objective value among all problem instances. We improve several existing results in the literature. First, we give an improved upper bound of the PoA for the scheduling game studied by Hoeksma and Uetz (WAOA’11 proceedings of the 9th international conference on approximation and online algorithms, vol 9. Springer, Berlin, pp 261–273, 2011). Then, we present a better lower bound of the PoA for the scheduling game studied by Lee et al. (Eur J Oper Res 220:305–313, 2012). Finally, we provide improved upper bounds of the PoA in terms of the number of machines, for another scheduling game proposed by Chen and Gürel (J Sched 15:157–164, 2012).

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Acknowledgements

The work of Yuzhong Zhang, Long Zhang and Qingguo Bai was supported in part by the National Natural Science Foundation of China under grants 11771251 and 71771138, the Natural Science Foundation of Shandong Province, China under grant ZR2017MG009, and the Key Project of Shandong Provincial Natural Science Foundation of China under grant ZR2015GZ009. The work of Donglei Du was supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC) Grant 283106 and National Science Foundation of China (NNSF) Grants (11771386 and 11728104).

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Authors and Affiliations

  1. Institute of Operations Research, School of Management, Qufu Normal University, Rizhao, 276826, Shandong, China

    Long Zhang, Yuzhong Zhang & Qingguo Bai

  2. Faculty of Business Administration, University of New Brunswick, Fredericton, NB, E3B 5A3, Canada

    Donglei Du

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  1. Long Zhang
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  2. Yuzhong Zhang
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Correspondence to Yuzhong Zhang.

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Zhang, L., Zhang, Y., Du, D. et al. Improved price of anarchy for machine scheduling games with coordination mechanisms. Optim Lett 13, 949–959 (2019). https://doi.org/10.1007/s11590-018-1285-3

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  • DOI: https://doi.org/10.1007/s11590-018-1285-3

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