The limits of smoothness: a primal-dual framework for price of anarchy bounds

Authors:
Uri Nadav;Tim Roughgarden
Affiliations:
Department of Computer Science, Stanford University, Stanford, CA;Department of Computer Science, Stanford University, Stanford, CA
Venue:
WINE'10 Proceedings of the 6th international conference on Internet and network economics
Year:
2010

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Abstract

We show a formal duality between certain equilibrium concepts, including the correlated and coarse correlated equilibrium, and analysis frameworks for proving bounds on the price of anarchy for such concepts. Our first application of this duality is a characterization of the set of distributions over game outcomes to which "smoothness bounds" always apply. This set is a natural and strict generalization of the coarse correlated equilibria of the game. Second, we derive a refined definition of smoothness that is specifically tailored for coarse correlated equilibria and can be used to give improved POA bounds for such equilibria.