The Price of Collusion in Series-Parallel Networks

We study the quality of equilibrium in atomic splittable routing games. We show that in single-source single-sink games on series-parallel graphs, the price of collusion — the ratio of the total delay of atomic Nash equilibrium to the Wardrop equilibrium — is at most 1. This proves that the existing bounds on the price of anarchy for Wardrop equilibria carry over to atomic splittable routing games in this setting.

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