Creative Commons Attribution 3.0 Unported license (CC-BY 3.0)when quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2014.242
URN: urn:nbn:de:0030-drops-47005
URL: https://drops.dagstuhl.de/opus/volltexte/2014/4700/
Hansknecht, Christoph ; Klimm, Max ; Skopalik, Alexander
Approximate Pure Nash Equilibria in Weighted Congestion Games
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Abstract
We study the existence of approximate pure Nash equilibria in weighted congestion games and develop techniques to obtain approximate potential functions that prove the existence of alpha-approximate pure Nash equilibria and the convergence of alpha-improvement steps. Specifically, we show how to obtain upper bounds for approximation factor alpha for a given class of cost functions. For example for concave cost functions the factor is at most 3/2, for quadratic cost functions it is at most 4/3, and for polynomial cost functions of maximal degree d it is at at most d + 1. For games with two players we obtain tight bounds which are as small as for example 1.054 in the case of quadratic cost functions.
BibTeX - Entry
@InProceedings{hansknecht_et_al:LIPIcs:2014:4700,
author = {Christoph Hansknecht and Max Klimm and Alexander Skopalik},
title = {{Approximate Pure Nash Equilibria in Weighted Congestion Games}},
booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014)},
pages = {242--257},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-74-3},
ISSN = {1868-8969},
year = {2014},
volume = {28},
editor = {Klaus Jansen and Jos{\'e} D. P. Rolim and Nikhil R. Devanur and Cristopher Moore},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2014/4700},
URN = {urn:nbn:de:0030-drops-47005},
doi = {10.4230/LIPIcs.APPROX-RANDOM.2014.242},
annote = {Keywords: Congestion game, Pure Nash equilibrium, Approximate equilibrium, Existence, Potential function}
}
| Keywords: | Congestion game, Pure Nash equilibrium, Approximate equilibrium, Existence, Potential function | |
| Seminar: | Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2014) | |
| Issue date: | 2014 | |
| Date of publication: | 04.09.2014 |
