@inproceedings{d606b32216a7422bbac181a2efbd0b90,
title = "Uniqueness of Equilibria in Atomic Splittable Polymatroid Congestion Games",
abstract = "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.",
author = "Tobias Harks and Veerle Timmermans",
note = "No data used",
year = "2016",
doi = "10.1007/978-3-319-45587-7_9",
language = "English",
isbn = "978-3-319-45586-0",
series = "Lecture Notes in Computer Science",
publisher = "Springer",
pages = "98--109",
editor = "R. Cerulli and Fujishige, {S. } and A. Mahjoub",
booktitle = "International Symposium on Combinatorial Optimization",
address = "United States",
}