NDLI: Local smoothness and the price of anarchy in atomic splittable congestion games

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Local smoothness and the price of anarchy in atomic splittable congestion games

Content Provider	ACM Digital Library
Author	Roughgarden, Tim Schoppmann, Florian
Abstract	We resolve the worst-case price of anarchy (POA) of atomic splittable congestion games. Prior to this work, no tight bounds on the POA in such games were known, even for the simplest non-trivial special case of affine cost functions. We make two distinct contributions. On the upper-bound side, we define the framework of "local smoothness", which refines the standard smoothness framework for games with convex strategy sets. While standard smoothness arguments cannot establish tight bounds on the POA in atomic splittable congestion games, we prove that local smoothness arguments can. Further, we prove that every POA bound derived via local smoothness applies automatically to every correlated equilibrium of the game. Unlike standard smoothness arguments, bounds proved using local smoothness do not always apply to the coarse correlated equilibria of the game. Our second contribution is a very general lower bound: for every set L that satisfies mild technical conditions, the worst-case POA of pure Nash equilibria in atomic splittable congestion games with cost functions in L is exactly the smallest upper bound provable using local smoothness arguments. In particular, the worst-case POA of pure Nash equilibria, mixed Nash equilibria, and correlated equilibria coincide in such games.
Starting Page	255
Ending Page	267
Page Count	13
File Format	PDF
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2011-01-23
Access Restriction	Subscribed
Content Type	Text
Resource Type	Article

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