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Scheduling Games with Machine-Dependent Priority Lists

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Web and Internet Economics (WINE 2019)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 11920))

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Abstract

We consider a scheduling game in which jobs try to minimize their completion time by choosing a machine to be processed on. Each machine uses an individual priority list to decide on the order according to which the jobs on the machine are processed. We characterize four classes of instances in which a pure Nash equilibrium (NE) is guaranteed to exist, and show by means of an example, that none of these characterizations can be relaxed. We then bound the performance of Nash equilibria for each of these classes with respect to the makespan of the schedule and the sum of completion times. We also analyze the computational complexity of several problems arising in this model. For instance, we prove that it is NP-hard to decide whether a NE exists, and that even for instances with identical machines, for which a NE is guaranteed to exist, it is NP-hard to approximate the best NE within a factor of \(2-\frac{1}{m}-\epsilon \) for every \(\epsilon >0\).

In addition, we study a generalized model in which players’ strategies are subsets of resources, where each resource has its own priority list over the players. We show that in this general model, even unweighted symmetric games may not have a pure NE, and we bound the price of anarchy with respect to the total players’ costs.

T. Tamir—This research is supported by The Israel Science Foundation (ISF). Grant No. 1036/17.

V. R. Vijayalakshmi—This work is supported by the German research council (DFG) Research Training Group 2236 UnRAVeL.

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Notes

  1. 1.

    For \(c=\frac{\sqrt{5}+1}{2}\), by taking \(w_b=c+\epsilon \), the PoS approaches \(1+c/(c+1)\) as \(\epsilon \rightarrow 0\).

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Authors and Affiliations

  1. Chair of Management Science, RWTH Aachen, Aachen, Germany

    Marc Schröder & Vipin Ravindran Vijayalakshmi

  2. School of Computer Science, The Interdisciplinary Center, Herzliya, Israel

    Tami Tamir

Authors
  1. Marc Schröder
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  2. Tami Tamir
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  3. Vipin Ravindran Vijayalakshmi
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Correspondence to Marc Schröder .

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Editors and Affiliations

  1. University of Patras, Rio, Greece

    Ioannis Caragiannis

  2. Google Research New York, New York, NY, USA

    Vahab Mirrokni

  3. The University of Texas System, Austin, TX, USA

    Evdokia Nikolova

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Schröder, M., Tamir, T., Ravindran Vijayalakshmi, V. (2019). Scheduling Games with Machine-Dependent Priority Lists. In: Caragiannis, I., Mirrokni, V., Nikolova, E. (eds) Web and Internet Economics. WINE 2019. Lecture Notes in Computer Science(), vol 11920. Springer, Cham. https://doi.org/10.1007/978-3-030-35389-6_21

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  • DOI: https://doi.org/10.1007/978-3-030-35389-6_21

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  • Online ISBN: 978-3-030-35389-6

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