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Semilinear Representations for Series-Parallel Atomic Congestion Games

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.
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hal-03937259 , version 1 (13-01-2023)

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Nathalie Bertrand, Nicolas Markey, Suman Sadhukhan, Ocan Sankur. Semilinear Representations for Series-Parallel Atomic Congestion Games. FSTTCS 2022 - 42nd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, Dec 2022, Chennai, France. pp.1-20, ⟨10.4230/LIPIcs.FSTTCS.2022.32⟩. ⟨hal-03937259⟩
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