We introduce the notion of an interpolation mechanism, that interpolates between a truthful and non-truthful mechanism. Specifically, an interpolation mechanism has two phases: in the first, bidders participate in some non-truthful mechanism, whose output is itself a truthful mechanism. In the second phase, bidders participate in the truthful mechanism selected during phase one.
In the first half of this talk, we provide a simple interpolation mechanism called the single-bid mechanism. Phase one of the single-bid mechanism asks each bidder to report a single real number, bi. In phase two, bidders are visited one at a time in decreasing order of bids, and are allowed to purchase any number of remaining items at bi per item. Contrary to other simple auction formats, such as sequential or simultaneous item auctions, bidders can actually implement no-regret learning strategies for the single-bid mechanism in poly-time. Therefore, price of anarchy bounds for correlated equilibria of the single-bid mechanism have more bite than their counterparts for other auction formats and equilibria which are not known to be computationally tractable. We further show that the single-bid auction has price of anarchy at most log(# items) at correlated equilibria.
In the second half of this talk, we will discuss interpolation mechanisms in more generality, and use tools from communication complexity to understand their limits. Specifically, we show that the approximation guarantee of the single-bid mechanism is tight for a quite broad class of interpolation mechanisms, meaning that any improvement would require significantly new ideas.
Based on joint works with Nikhil Devanur, Jamie Morgenstern and Vasilis Syrgkanis, and Mark Braverman and Jieming Mao.