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Proceedings Article, Paper
@InProceedings
Beitrag in Tagungsband, Workshop

Author, Editor
Author(s):
Vidali, Angelinadblp
Editor(s):
Leonardi, Stefanodblp
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
Note, Abstract, ©
(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

Correlation
MPG Unit:
Max-Planck-Institut für Informatik
MPG Subunit:
Algorithms and Complexity Group
Appearance:
MPII WWW Server, MPII FTP Server, MPG publications list, university publications list, working group publication list, Fachbeirat, VG Wort



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},
 ADDRESS = {Rome, Italy},
 ISBN = {978-3-642-10840-2},
 DOI = {10.1007/978-3-642-10841-9_31},
}

Entry last modified by Anja Becker, 03/09/2010
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Editor(s)
[Library]		Created
01/26/2010 18:18:25
Revision
1.
0.


Editor
Anja Becker
Angelina Vidali


Edit Date
09.03.2010 15:02:30
26.01.2010 18:18:25