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 Proceedings Article, Paper @InProceedings Beitrag in Tagungsband, Workshop
 Author, Editor
 Author(s): Vidali, Angelina dblp
 Editor(s): Leonardi, Stefano dblp Not MPII Editor(s): Leonardi, Stefano
 BibTeX cite key*: Vidali2009
 Title, Booktitle
 Title*: The Geometry of Truthfulness Booktitle*: Internet and Network Economics : 5th International Workshop, WINE 2009
 Event, URLs
 Conference URL:: http://www.dis.uniroma1.it/~wine09/ Downloading URL: http://www.mpi-inf.mpg.de/~angelina/geometrytruth.pdf Event Address*: Rome, Italy Language: English Event Date* (no longer used): Organization: Event Start Date: 14 December 2009 Event End Date: 18 December 2009
 Publisher
 Name*: Springer URL: http://www.springer.com/computer/lncs?SGWID=0-164-6-737109-0 Address*: Berlin, Germany Type:
 Vol, No, Year, pp.
 Series: Lecture Notes in Computer Science
 Volume: 5929 Number: Month: Pages: 340-350 Year*: 2009 VG Wort Pages: ISBN/ISSN: 978-3-642-10840-2 Sequence Number: DOI: 10.1007/978-3-642-10841-9_31
 (LaTeX) Abstract: We study the geometrical shape of the partitions of the input space created by the allocation rule of a truthful mechanism for multi-unit auctions with multidimensional types and additive quasilinear utilities. We introduce a new method for describing the the allocation graph and the geometry of truthful mechanisms for an arbitrary number of items(/tasks). Applying this method we characterize all possible mechanisms for the case of three items. Previous work shows that Monotonicity is a necessary and sufficient condition for truthfulness in convex domains. If there is only one item, monotonicity is the most practical description of truthfulness we could hope for, however for the case of more than two items and additive valuations (like in the scheduling domain) we would need a global and more intuitive description, hopefully also practical for proving lower bounds. We replace Monotonicity by a geometrical and global characterization of truthfulness. Our results apply directly to the scheduling unrelated machines problem. Until now such a characterization was only known for the case of two tasks. It was one of the tools used for proving a lower bound of $1+\sqrt{2}$ for the case of 3 players. This makes our work potentially useful for obtaining improved lower bounds for this very important problem. Finally we show lower bounds of $1+\sqrt{n}$ and $n$ respectively for two special classes of scheduling mechanisms, defined in terms of their geometry, demonstrating how geometrical considerations can lead to lower bound proofs. Download Access Level: Public

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BibTeX Entry:

@INPROCEEDINGS{Vidali2009,
AUTHOR = {Vidali, Angelina},
EDITOR = {Leonardi, Stefano},
TITLE = {The Geometry of Truthfulness},
BOOKTITLE = {Internet and Network Economics : 5th International Workshop, WINE 2009},
PUBLISHER = {Springer},
YEAR = {2009},
VOLUME = {5929},
PAGES = {340--350},
SERIES = {Lecture Notes in Computer Science},
ISBN = {978-3-642-10840-2},
DOI = {10.1007/978-3-642-10841-9_31},
}