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

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Combinatorial Optimization and Applications (COCOA 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10628))

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.

For a full version of this work see [8].

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Authors and Affiliations

  1. School of Management, Xi’an Jiaotong University, Xi’an, China

    Cong Chen & Yinfeng Xu

  2. Department of Computer Science, ETH Zurich, Zurich, Switzerland

    Cong Chen & Paolo Penna

Authors
  1. Cong Chen
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  2. Paolo Penna
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  3. Yinfeng Xu
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Correspondence to Cong Chen .

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Editors and Affiliations

  1. Shanghai Jiao Tong University, Shanghai, China

    Xiaofeng Gao

  2. Harbin Institute of Technology, Shenzhen, China

    Hongwei Du

  3. Kennesaw State University, Kennesaw, Georgia, USA

    Meng Han

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Chen, C., Penna, P., Xu, Y. (2017). Selfish Jobs with Favorite Machines: Price of Anarchy vs. Strong Price of Anarchy. In: Gao, X., Du, H., Han, M. (eds) Combinatorial Optimization and Applications. COCOA 2017. Lecture Notes in Computer Science(), vol 10628. Springer, Cham. https://doi.org/10.1007/978-3-319-71147-8_16

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  • DOI: https://doi.org/10.1007/978-3-319-71147-8_16

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  • Online ISBN: 978-3-319-71147-8

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