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DOI: 10.4230/LIPIcs.ICALP.2019.133
URN: urn:nbn:de:0030-drops-107095
URL: http://drops.dagstuhl.de/opus/volltexte/2019/10709/
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Caragiannis, Ioannis ; Fanelli, Angelo

On Approximate Pure Nash Equilibria in Weighted Congestion Games with Polynomial Latencies

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Abstract

We consider the problem of the existence of natural improvement dynamics leading to approximate pure Nash equilibria, with a reasonable small approximation, and the problem of bounding the efficiency of such equilibria in the fundamental framework of weighted congestion game with polynomial latencies of degree at most d >= 1. In this work, by exploiting a simple technique, we firstly show that the game always admits a d-approximate potential function. This implies that every sequence of d-approximate improvement moves by the players always leads the game to a d-approximate pure Nash equilibrium. As a corollary, we also obtain that, under mild assumptions on the structure of the players' strategies, the game always admits a constant approximate potential function. Secondly, by using a simple potential function argument, we are able to show that in the game there always exists a (d+delta)-approximate pure Nash equilibrium, with delta in [0,1], whose cost is 2/(1+delta) times the cost of an optimal state.

BibTeX - Entry

@InProceedings{caragiannis_et_al:LIPIcs:2019:10709,
  author =	{Ioannis Caragiannis and Angelo Fanelli},
  title =	{{On Approximate Pure Nash Equilibria in Weighted Congestion Games with Polynomial Latencies}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{133:1--133:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Christel Baier and Ioannis Chatzigiannakis and Paola Flocchini and Stefano Leonardi},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10709},
  URN =		{urn:nbn:de:0030-drops-107095},
  doi =		{10.4230/LIPIcs.ICALP.2019.133},
  annote =	{Keywords: Congestion games, approximate pure Nash equilibrium, potential functions, approximate price of stability}
}

Keywords: Congestion games, approximate pure Nash equilibrium, potential functions, approximate price of stability
Seminar: 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)
Issue Date: 2019
Date of publication: 08.07.2019


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