eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2014-09-04
242
257
10.4230/LIPIcs.APPROX-RANDOM.2014.242
article
Approximate Pure Nash Equilibria in Weighted Congestion Games
Hansknecht, Christoph
Klimm, Max
Skopalik, Alexander
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol028-approx-random2014/LIPIcs.APPROX-RANDOM.2014.242/LIPIcs.APPROX-RANDOM.2014.242.pdf
Congestion game
Pure Nash equilibrium
Approximate equilibrium
Existence
Potential function