The primal framework II: smoothness

The Primal Framework II: Smoothness

This is the second in a series of articles developing abstract classification theory for classes that have a notion of prime models over independent pairs and over chains. It deals with the problem of smoothness and establishing the existence and uniqueness of a ‘monster model’. We work here with a predicate for a canonically prime model. In a forthcoming paper, entitled, ‘Abstract classes with...

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

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 gener...

The Primal Framework I

Bayesian Games and the Smoothness Framework

We consider a general class of Bayesian Games where each players utility depends on his type (possibly multidimensional) and on the strategy profile and where players’ types are distributed independently. We show that if their full information version for any fixed instance of the type profile is a smooth game then the Price of Anarchy bound implied by the smoothness property, carries over to t...

A Hyperelliptic Smoothness Test, Ii