Noun

Singular Vickrey auction

Plural Vickrey auctions

Vickrey auction (plural Vickrey auctions)

1. A type of sealed-bid auction, where bidders submit written bids without knowing the bids of others, in which the highest bidder wins but the price paid is the second-highest bid.

A Vickrey auction is a type of sealed-bid auction, where bidders submit written bids without knowing the bid of the other people in the auction. The highest bidder wins, but the price paid is the second-highest bid. The auction was created by William Vickrey. This type of auction is strategically similar to an English auction, and gives bidders an incentive to bid their true value.

Vickrey's original paper considered only auctions where a single, indivisible good is being sold. In this case, the terms Vickrey auction and second-price sealed-bid auction are equivalent, and are used interchangeably. When multiple identical units (or a divisible good) are being sold in a single auction, the most obvious generalization is to have all winning bidders pay the amount of the highest non-winning bid. This is known as a uniform price auction. The uniform-price auction does not, however, result in bidders bidding their true valuations as they do in a second-price auction unless each bidder has demand for only a single unit.

A generalization of the Vickrey auction that maintains the incentive to bid truthfully is known as the Vickrey–Clarke–Groves (VCG) mechanism. The idea in VCG is that each player in the auction pays the opportunity cost that their presence introduces to all the other players. For example, suppose two apples are being auctioned among three bidders. Bidder A wants one apple and bids $5 for that apple. Bidder B wants one apple and is willing to pay $2 for it. Bidder C wants two apples and is willing to pay $6 to have both of them, but is uninterested in buying only one without the other. First, the outcome of the auction is determined by maximizing bids: the apples go to bidder A and bidder B. Next, to decide payments, the opportunity cost each bidder imposed on the rest of the bidders is considered. Currently, B has a utility of $2. If bidder A had not been present, C would have won, and had a utility of $6, so A pays $6–$2 = $4. For the payment of bidder B: currently A has a utility of $5 and C has a utility of 0. If bidder B had been absent, C would have won and had a utility of $6, so B pays $6–$5 = $1. The outcome is identical whether or not bidder C participates, so C does not need to pay anything.

Vickrey auctions are much studied in economic literature, but are not particularly common in practice. One market in which they have been used is stamp collecting. eBay's system of proxy bidding is similar, but not identical, to a Vickrey auction. A slight generalized variant of a Vickrey auction, named generalized second-price auction, which is different from the VCG mechanism, is known to be used in Google's and Yahoo!'s online advertisement programmes. NYU Law School uses an iterated version of the Vickrey auction model for its course registration lottery.