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Weighted congestion games: price of anarchy, universal worst-case examples, and tightness. (English) Zbl 1287.91026
de Berg, Mark (ed.) et al., Algorithms – ESA 2010. 18th annual European symposium, Liverpool, UK, September 6–8, 2010. Proceedings, Part II. Berlin: Springer (ISBN 978-3-642-15780-6/pbk). Lecture Notes in Computer Science 6347, 17-28 (2010).
Summary: We characterize the price of anarchy in weighted congestion games, as a function of the allowable resource cost functions. Our results provide as thorough an understanding of this quantity as is already known for nonatomic and unweighted congestion games, and take the form of universal (cost function-independent) worst-case examples. One noteworthy byproduct of our proofs is the fact that weighted congestion games are “tight”, which implies that the worst-case price of anarchy with respect to pure Nash, mixed Nash, correlated, and coarse correlated equilibria are always equal (under mild conditions on the allowable cost functions). Another is the fact that, like nonatomic but unlike atomic (unweighted) congestion games, weighted congestion games with trivial structure already realize the worst-case POA, at least for polynomial cost functions.
We also prove a new result about unweighted congestion games: the worst-case price of anarchy in symmetric games is, as the number of players goes to infinity, as large as in their more general asymmetric counterparts.
For the entire collection see [Zbl 1194.68068].

91A43 Games involving graphs
91B32 Resource and cost allocation (including fair division, apportionment, etc.)
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