Internet and Network Economics

Volume 6484 of the series Lecture Notes in Computer Science pp 319-326

The Limits of Smoothness: A Primal-Dual Framework for Price of Anarchy Bounds

  • Uri NadavAffiliated withDepartment of Computer Science, Stanford University
  • , Tim RoughgardenAffiliated withDepartment of Computer Science, Stanford University

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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.