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A Unifying Approximate Potential for Weighted Congestion Games

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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.

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Acknowledgements

We thank Martin Gairing for interesting discussions.

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Authors and Affiliations

  1. Department of Data Science, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Cauerstrasse 11, Erlangen, 91058, Bayern, Germany

    Yiannis Giannakopoulos

  2. LASIGE, Departamento de Informática, Faculdade de Ciências, Universidade de Lisboa, 1749–016, Lisboa, Portugal

    Diogo Poças

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

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Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

A significant part of this work was done while Y. Giannakopoulos and D. Poças were members of the Operations Research group at TU Munich, supported by the Alexander von Humboldt Foundation with funds from the German Federal Ministry of Education and Research (BMBF). D. Poças was also supported by FCT via LASIGE Research Unit, ref. UIDB/00408/2020 and ref. UIDP/00408/2020.

A preliminary version of this paper appeared in SAGT’20 [1].

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Giannakopoulos, Y., Poças, D. A Unifying Approximate Potential for Weighted Congestion Games. Theory Comput Syst 67, 855–876 (2023). https://doi.org/10.1007/s00224-023-10133-z

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