License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2018.14
URN: urn:nbn:de:0030-drops-85092
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8509/
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Bilò, Davide ; Lenzner, Pascal

On the Tree Conjecture for the Network Creation Game

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LIPIcs-STACS-2018-14.pdf (0.7 MB)

Abstract

Selfish Network Creation focuses on modeling real world networks from a game-theoretic point of view. One of the classic models by Fabrikant et al.[PODC'03] is the network creation game, where agents correspond to nodes in a network which buy incident edges for the price of alpha per edge to minimize their total distance to all other nodes. The model is well-studied but still has intriguing open problems. The most famous conjectures state that the price of anarchy is constant for all alpha and that for alpha >= n all equilibrium networks are trees.

We introduce a novel technique for analyzing stable networks for high edge-price alpha and employ it to improve on the best known bounds for both conjectures. In particular we show that for alpha > 4n-13 all equilibrium networks must be trees, which implies a constant price of anarchy for this range of alpha. Moreover, we also improve the constant upper bound on the price of anarchy for equilibrium trees.

BibTeX - Entry

@InProceedings{bil_et_al:LIPIcs:2018:8509,
  author =	{Davide Bil{\`o} and Pascal Lenzner},
  title =	{{On the Tree Conjecture for the Network Creation Game}},
  booktitle =	{35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)},
  pages =	{14:1--14:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-062-0},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{96},
  editor =	{Rolf Niedermeier and Brigitte Vall{\'e}e},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8509},
  URN =		{urn:nbn:de:0030-drops-85092},
  doi =		{10.4230/LIPIcs.STACS.2018.14},
  annote =	{Keywords: Algorithmic Game Theory, Network Creation Game, Price of Anarchy, Quality of Nash Equilibria}
}

Keywords: Algorithmic Game Theory, Network Creation Game, Price of Anarchy, Quality of Nash Equilibria
Collection: 35th Symposium on Theoretical Aspects of Computer Science (STACS 2018)
Issue Date: 2018
Date of publication: 27.02.2018

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