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.
Original language | English |
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Pages (from-to) | 812-830 |
Number of pages | 19 |
Journal | Journal of Combinatorial Optimization |
Volume | 36 |
Issue number | 3 |
DOIs | |
Publication status | Published - 1 Oct 2018 |
Keywords
- Polymatroid
- Congestion game
- Uniqueness of equilibria
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