The Impact of Social Ignorance on Weighted Congestion Games

Fotakis, D; Gkatzelis, V; Kaporis, AC; Spirakis, PG

dc.contributor.author	Fotakis, D	en
dc.contributor.author	Gkatzelis, V	en
dc.contributor.author	Kaporis, AC	en
dc.contributor.author	Spirakis, PG	en
dc.date.accessioned	2014-03-01T02:14:49Z
dc.date.available	2014-03-01T02:14:49Z
dc.date.issued	2012	en
dc.identifier.issn	14324350	en
dc.identifier.uri	https://dspace.lib.ntua.gr/xmlui/handle/123456789/30131
dc.subject	Algorithmic game theory	en
dc.subject	Congestion games	en
dc.subject	Price of anarchy	en
dc.title	The Impact of Social Ignorance on Weighted Congestion Games	en
heal.type	journalArticle	en
heal.identifier.primary	10.1007/s00224-011-9355-2	en
heal.identifier.secondary	http://dx.doi.org/10.1007/s00224-011-9355-2	en
heal.publicationDate	2012	en
heal.abstract	We consider weighted linear congestion games, and investigate how social ignorance, namely lack of information about the presence of some players, affects the inefficiency of pure Nash equilibria (PNE) and the convergence rate of the ε-Nash dynamics. To this end, we adopt the model of graphical linear congestion games with weighted players, where the individual cost and the strategy selection of each player only depends on his neighboring players in the social graph. We show that such games admit a potential function, and thus a PNE. Next, we investigate the Price of Anarchy (PoA) and the Price of Stability (PoS) of graphical linear congestion games with respect to the players' total actual cost. Our main result is that the impact of social ignorance on the PoA and on the PoS is naturally quantified by the independence numberα(G) of the social graph G. In particular, we show that the PoA grows roughly as α(G)(α(G)+2), which is essentially tight as long as α(G) does not exceed half the number of players, and that the PoS lies between α(G) and 2α(G). Moreover, we show that the ε-Nash dynamics reaches an α(G)(α(G)+2)-approximate configuration in polynomial time that does not directly depend on the social graph. For unweighted graphical linear games with symmetric strategies, we show that the ε-Nash dynamics reaches an ε-approximate PNE in polynomial time that exceeds the corresponding time for symmetric linear games by a factor at most as large as the number of players. © 2011 Springer Science+Business Media, LLC.	en
heal.journalName	Theory of Computing Systems	en
dc.identifier.doi	10.1007/s00224-011-9355-2	en
dc.identifier.volume	50	en
dc.identifier.issue	3	en
dc.identifier.spage	559	en
dc.identifier.epage	578	en