Partial Verification as a Substitute for Money

Recent work shows that we can use partial verification instead of money to implement truthful mechanisms. In this paper we develop tools to answer the following question. Given an allocation rule that can be made truthful with payments, what is the minimal verification needed to make it truthful without them? Our techniques leverage the geometric relationship between the type space and the set of possible allocations.Comment: Extended Version of 'Partial Verification as a Substitute for Money', AAAI 201

Truthful approximation mechanisms for restricted combinatorial auctions

When attempting to design a truthful mechanism for a computationally hard problem such as combinatorial auctions, one is faced with the problem that most efficiently computable heuristics can not be embedded in any truthful mechanism (e.g. VCG-like payment rules will not ensure truthfulness). We develop a set of techniques that allow constructing efficiently computable truthful mechanisms for combinatorial auctions in the special case where each bidder desires a specific known subset of items and only the valuation is unknown by the mechanism (the single parameter case). For this case we extend the work of Lehmann, O'Callaghan, and Shoham, who presented greedy heuristics. We show how to use If-Then-Else constructs, perform a partial search, and use the LP relaxation. We apply these techniques for several canonical types of combinatorial auctions, obtaining truthful mechanisms with provable approximation ratios

An Overview of Combinatorial Auctions

An auction is combinatorial when bidders can place bids on combinations of items, called “packages,” rather than just individual items. Computer scientists are interested in combinatorial auctions because they are concerned with the expressiveness of bidding languages, as well as the algorithmic aspects of the underlying combinatorial problem. The combinatorial problem has attracted attention from operations researchers, especially those working in combinatorial optimization and mathematical programming, who are fascinated by the idea of applying these tools to auctions. Auctions have been studied extensively by economists, of course. Thus, the newly emerging field of combinatorial auctions lies at the intersection of computer science, operations research, and economics. In this article, we present a brief introduction to combinatorial auctions, based on our book, Combinatorial Auctions (MIT Press, 2006), in which we look at combinatorial auctions from all three perspectives.Auctions