Equilibria of Atomic Flow Games are not Unique

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Previous chapter Next chapter Full AccessProceedings Proceedings of the 2009 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)Equilibria of Atomic Flow Games are not UniqueUmang Bhaskar, Lisa Fleischer, Darrell Hoy, and Chien-Chung HuangUmang Bhaskar, Lisa Fleischer, Darrell Hoy, and Chien-Chung Huangpp.748 - 757Chapter DOI:https://doi.org/10.1137/1.9781611973068.82PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstract In routing games with infinitesimal players, it follows from well-known convexity arguments that equilibria exist and are unique (up to induced delays, and under weak assumptions on delay functions). In routing games with players that control large amounts of flow, uniqueness has been demonstrated only in limited cases: in 2-terminal, nearly-parallel graphs; when all players control exactly the same amount of flow; when latency functions are polynomials of degree at most three. In this work, we answer an open question posed by Cominetti, Correa, and Stier-Moses (ICALP 2006) and show that there may be multiple equilibria in atomic player routing games. We demonstrate this multiplicity via two specific examples. In addition, we show our examples are topologically minimal by giving a complete characterization of the class of network topologies for which unique equilibria exist. Our proofs and examples are based on a novel characterization of these topologies in terms of sets of circulations. Previous chapter Next chapter RelatedDetails Published:2009ISBN:978-0-89871-680-1eISBN:978-1-61197-306-8 https://doi.org/10.1137/1.9781611973068Book Series Name:ProceedingsBook Code:PR132Book Pages:xviii + 1288