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DOI: 10.4230/LIPIcs.ICALP.2019.133
URN: urn:nbn:de:0030-drops-107095
URL: https://drops.dagstuhl.de/opus/volltexte/2019/10709/
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: | 04.07.2019 |
