On the Inefficiency of Standard Multi-Unit Auctions

We study two standard multi-unit auction formats for allocating multiple units of asingle good to multi-demand bidders. The first one is the Discriminatory Auction, whichcharges every winner his winning bids. The second is the Uniform Price Auction, whichdetermines a uniform price to be paid per unit. Variants of both formats find applicationsranging from the allocation of state bonds to investors, to online sales over the internet,facilitated by popular online brokers.For these formats, we consider two bidding interfaces: (i) standard bidding, which ismost prevalent in the scientific literature, and (ii) uniform bidding, which is more popularin practice. In this work, we evaluate the economic inefficiency of both multi-unit auctionformats for both bidding interfaces, by means of upper and lower bounds on the Priceof Anarchy for pure Nash equilibria and mixed Bayes-Nash equilibria. Our developmentsimprove significantly upon bounds that have been obtained recently in [Markakis, Telelis,SAGT 2012] and [Syrgkanis, Tardos, STOC 2013] for submodular valuation functions.Moreover, we consider for the first time bidders with subadditive valuation functions forthese auction formats. Our results signify that these auctions are nearly efficient, whichprovides further justification for their use in practice.