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A Unifying Approximate Potential for Weighted Congestion Games

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Algorithmic Game Theory (SAGT 2020)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 12283))

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Abstract

We provide a unifying, black-box tool for establishing existence of approximate equilibria in weighted congestion games and, at the same time, bounding their Price of Stability. Our framework can handle resources with general costs—including, in particular, decreasing ones—and is formulated in terms of a set of parameters which are determined via elementary analytic properties of the cost functions.

We demonstrate the power of our tool by applying it to recover the recent result of Caragiannis and Fanelli [ICALP’19] for polynomial congestion games; improve upon the bounds for fair cost sharing games by Chen and Roughgarden [Theory Comput. Syst., 2009]; and derive new bounds for nondecreasing concave costs. An interesting feature of our framework is that it can be readily applied to mixtures of different families of cost functions; for example, we provide bounds for games whose resources are conical combinations of polynomial and concave costs.

In the core of our analysis lies the use of a unifying approximate potential function which is simple and general enough to be applicable to arbitrary congestion games, but at the same time powerful enough to produce state-of-the-art bounds across a range of different cost functions.

Supported by the Alexander von Humboldt Foundation with funds from the German Federal Ministry of Education and Research (BMBF). Y. Giannakopoulos is an associated researcher with the Research Training Group GRK 2201 “Advanced Optimization in a Networked Economy”, funded by the German Research Foundation (DFG). A full version of this paper is available at  [16]: https://arxiv.org/abs/2005.10101.

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Acknowledgements

We thank Martin Gairing for interesting discussions.

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Authors and Affiliations

  1. TU Munich, Munich, Germany

    Yiannis Giannakopoulos & Diogo Poças

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  1. Yiannis Giannakopoulos
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  2. Diogo Poças
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Correspondence to Yiannis Giannakopoulos .

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Editors and Affiliations

  1. Institute of Mathematics, Augsburg University, Augsburg, Germany

    Tobias Harks

  2. Institute of Mathematics, Technical University Berlin, Berlin, Germany

    Max Klimm

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Giannakopoulos, Y., Poças, D. (2020). A Unifying Approximate Potential for Weighted Congestion Games. In: Harks, T., Klimm, M. (eds) Algorithmic Game Theory. SAGT 2020. Lecture Notes in Computer Science(), vol 12283. Springer, Cham. https://doi.org/10.1007/978-3-030-57980-7_7

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  • DOI: https://doi.org/10.1007/978-3-030-57980-7_7

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