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Commodity Auctions and Frugality Ratios
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BibTeX
@MISC{Goldberg_commodityauctions,
author = {Paul W. Goldberg and Antony Mccabe},
title = {Commodity Auctions and Frugality Ratios},
year = {}
}
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Abstract
Abstract. We study set-system auctions whereby a single buyer wants to purchase Q items of some commodity. There are multiple sellers, each of whom has some known number of items, and a private cost for supplying those items. Thus a “feasible set ” of sellers (a set that is able to comprise the winning bidders) is any set of sellers whose total quantity sums to at least Q. Weshowthat,eveninalimitedspecialcase,VCG has a frugality ratio of at least n−1 (withrespecttotheNTUminbenchmark) and that this matches the upper bound for any set-system auction. We show a lower bound on the frugality of any truthful mechanism of Q in this setting and give a truthful mechanism with a frugality ratio of 2 √ Q.However,weshowthatsimilartypesof‘scaling’mechanism,in the general (integer) case, give a frugality ratio of at least 4Qe−2 ln 2 Q. 1
