Uniqueness of Equilibria in Atomic Splittable Polymatroid Congestion Games

Tobias Harks, Veerle Timmermans*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review


We study uniqueness of nash equilibria in atomic splittable congestion games and derive a uniqueness result based on polymatroid theory: when the strategy space of every player is a bidirectional flow polymatroid, then equilibria are unique. Bidirectional flow polymatroids are introduced as a subclass of polymatroids possessing certain exchange properties. We show that important cases such as base orderable matroids can be recovered as a special case of bidirectional flow polymatroids. On the other hand we show that matroidal set systems are in some sense necessary to guarantee uniqueness of equilibria: for every atomic splittable congestion game with at least three players and non-matroidal set systems per player, there is an isomorphic game having multiple equilibria. Our results leave a gap between base orderable matroids and general matroids for which we do not know whether equilibria are unique.
Original languageEnglish
Title of host publicationInternational Symposium on Combinatorial Optimization
Subtitle of host publicationISCO 2016: Combinatorial Optimization
EditorsR. Cerulli, S. Fujishige, A. Mahjoub
ISBN (Electronic)978-3-319-45587-7
ISBN (Print)978-3-319-45586-0
Publication statusPublished - 2016

Publication series

SeriesLecture Notes in Computer Science

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