License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.FSTTCS.2022.32
URN: urn:nbn:de:0030-drops-174243
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2022/17424/
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Bertrand, Nathalie ; Markey, Nicolas ; Sadhukhan, Suman ; Sankur, Ocan

Semilinear Representations for Series-Parallel Atomic Congestion Games

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Abstract

We consider atomic congestion games on series-parallel networks, and study the structure of the sets of Nash equilibria and social local optima on a given network when the number of players varies. We establish that these sets are definable in Presburger arithmetic and that they admit semilinear representations whose all period vectors have a common direction. As an application, we prove that the prices of anarchy and stability converge to 1 as the number of players goes to infinity, and show how to exploit these semilinear representations to compute these ratios precisely for a given network and number of players.

BibTeX - Entry

@InProceedings{bertrand_et_al:LIPIcs.FSTTCS.2022.32,
  author =	{Bertrand, Nathalie and Markey, Nicolas and Sadhukhan, Suman and Sankur, Ocan},
  title =	{{Semilinear Representations for Series-Parallel Atomic Congestion Games}},
  booktitle =	{42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)},
  pages =	{32:1--32:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-261-7},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{250},
  editor =	{Dawar, Anuj and Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2022/17424},
  URN =		{urn:nbn:de:0030-drops-174243},
  doi =		{10.4230/LIPIcs.FSTTCS.2022.32},
  annote =	{Keywords: congestion games, Nash equilibria, Presburger arithmetic, semilinear sets, price of anarchy}
}

Keywords: congestion games, Nash equilibria, Presburger arithmetic, semilinear sets, price of anarchy
Collection: 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022)
Issue Date: 2022
Date of publication: 14.12.2022

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