CS364B: Frontiers in Mechanism Design Lecture #20: Characterization of Revenue-Maximizing Auctions

Recall what we are shooting for: a multi-parameter analog of Myerson’s theory of revenuemaximizing optimal auctions. Single-parameter optimal mechanisms are virtual welfare maximizers. We’ve seen that multi-parameter optimal mechanisms are generally randomized. It would seem that the coolest statement that could be true is: revenue-maximizing optimal auctions for multi-parameter problems are always distributions over virtual welfare maximizers. This lecture identifies conditions under which this coolest-possible statement is actually true. Recall that the reduced form (y,q) induced by a direct-revelation mechanism (x,p) consists of an interim allocation rule y defined by