Simple unit-price auction procedures

This paper proposes four unit-price auction procedures with multiple heterogeneous items: the pay-your-bid auction, the lowest-winner’s-bid auction, the highest-loser’s auction, and the pay the next highest bid to yours auction.  Our model is the same as the one analyzed by Varian (2007) and Edelman, Ostrovsky, and Schwarz (2007) and is a special case of Baba (1997) and Baba (1998) which assume that the value of the item is supermodular with respect to a bidder’s type and a public signal and multiplication is a special example of supermodularity.  All four unit-price auction procedures with aprropriate reserve prices yield the same expected revenue to the seller and implement the optimal auction under the assumptions of unit demand, indivisible items, no collusive behavior, and risk-neutrality of bidders and the seller.  Further, the lowest-winner’s auction and the highest-loser’s auction satisfy a fair criterion in the sense that each winner pays the same unit-price regardless of the item s/he wins.  In addition to internet keyword auctions, a wide range of procurement auctions such as road repair contracts and school districts’ milk procurement are applications of our model.  The lowest-winner’s-bid auction and the highest-loser’s-bid auction are desirable for public procurement contracts because of their satisfying fair criterion and robustness against collusion in addition to their achieving efficient allocation and implementing the optimal auction mechanism.  The model is applicable to Google’s advertisement slot auctions, spectrum auctions, airport slot auctions, road repair auctions, and various other privatization and procurement auctions.

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