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Semilinear Representations for Series-Parallel Atomic Congestion Games

Authors Nathalie Bertrand , Nicolas Markey , Suman Sadhukhan, Ocan Sankur

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Author Details

Nathalie Bertrand
  • Univ Rennes, Inria, CNRS, IRISA, France
Nicolas Markey
  • Univ Rennes, Inria, CNRS, IRISA, France
Suman Sadhukhan
  • Univ Rennes, Inria, CNRS, IRISA, France
  • University of Haifa, Israel
Ocan Sankur
  • Univ Rennes, Inria, CNRS, IRISA, France

Funding

This research was partially supported by ISF grant no. 1679/21.

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Nathalie Bertrand, Nicolas Markey, Suman Sadhukhan, and Ocan Sankur. Semilinear Representations for Series-Parallel Atomic Congestion Games. In 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 250, pp. 32:1-32:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.FSTTCS.2022.32

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Algorithmic game theory
  • Theory of computation → Solution concepts in game theory
Keywords
  • congestion games
  • Nash equilibria
  • Presburger arithmetic
  • semilinear sets
  • price of anarchy

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