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Computing Approximate Pure Nash Equilibria in Shapley Value Weighted Congestion Games

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Web and Internet Economics (WINE 2017)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 10660))

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Abstract

We study the computation of approximate pure Nash equilibria in Shapley value (SV) weighted congestion games, introduced in [19]. This class of games considers weighted congestion games in which Shapley values are used as an alternative (to proportional shares) for distributing the total cost of each resource among its users. We focus on the interesting subclass of such games with polynomial resource cost functions and present an algorithm that computes approximate pure Nash equilibria with a polynomial number of strategy updates. Since computing a single strategy update is hard, we apply sampling techniques which allow us to achieve polynomial running time. The algorithm builds on the algorithmic ideas of [7], however, to the best of our knowledge, this is the first algorithmic result on computation of approximate equilibria using other than proportional shares as player costs in this setting. We present a novel relation that approximates the Shapley value of a player by her proportional share and vice versa. As side results, we upper bound the approximate price of anarchy of such games and significantly improve the best known factor for computing approximate pure Nash equilibria in weighted congestion games of [7].

This work was partially supported by the German Research Foundation (DFG) within the Collaborative Research Centre “On-The-Fly Computing” (SFB 901) and by EPSRC grant EP/L011018/1.

The full version of this paper is available at http://arxiv.org/abs/1710.01634.

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Notes

  1. 1.

    Note that in the unweighted case, proportional sharing and Shapley cost sharing coincide.

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Author information

Authors and Affiliations

  1. Paderborn University, Paderborn, Germany

    Matthias Feldotto & Alexander Skopalik

  2. University of Liverpool, Liverpool, UK

    Martin Gairing

  3. King’s College London, London, UK

    Grammateia Kotsialou

Authors
  1. Matthias Feldotto
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  2. Martin Gairing
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  3. Grammateia Kotsialou
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  4. Alexander Skopalik
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Corresponding author

Correspondence to Matthias Feldotto .

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Editors and Affiliations

  1. Microsoft Research, Redmond, Washington, USA

    Nikhil R. Devanur

  2. Shanghai University of Finance and Economics, Shanghai, China

    Pinyan Lu

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Feldotto, M., Gairing, M., Kotsialou, G., Skopalik, A. (2017). Computing Approximate Pure Nash Equilibria in Shapley Value Weighted Congestion Games. In: R. Devanur, N., Lu, P. (eds) Web and Internet Economics. WINE 2017. Lecture Notes in Computer Science(), vol 10660. Springer, Cham. https://doi.org/10.1007/978-3-319-71924-5_14

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  • DOI: https://doi.org/10.1007/978-3-319-71924-5_14

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