Uniqueness of equilibria in atomic splittable polymatroid congestion games

Tobias Harks () and Veerle Timmermans ()
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Tobias Harks: University of Augsburg
Veerle Timmermans: Maastricht University

Journal of Combinatorial Optimization, 2018, vol. 36, issue 3, No 7, 812-830

Abstract: 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.

Keywords: Polymatroid; Congestion game; Uniqueness of equilibria (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10878-017-0166-5

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