The highest bidder wins but the price paid is the second-highest bid.
The auction was first described academically by Columbia University professor William Vickrey in 1961[1] though it had been used by stamp collectors since 1893.
[2] In 1797 Johann Wolfgang von Goethe sold a manuscript using a sealed-bid, second-price auction.
[3] Vickrey's original paper mainly considered auctions where only a single, indivisible good is being sold.
In the case of multiple identical goods, the bidders submit inverse demand curves and pay the opportunity cost.
[4] Vickrey auctions are much studied in economic literature but uncommon in practice.
In a Vickrey auction with private values each bidder maximizes their expected utility by bidding (revealing) their valuation of the item for sale.
These type of auctions are sometimes used for specified pool trading in the agency mortgage-backed securities (MBS) market.
A Vickrey auction is decision efficient (the winner is the bidder with the highest valuation) under the most general circumstances;[citation needed] it thus provides a baseline model against which the efficiency properties of other types of auctions can be posited.
The high bidder is awarded the item and pays his or her bid.
and the buyer is not the current high bidder, it is more profitable to bid than to let someone else be the winner.
Thus it is a dominant strategy for a buyer to drop out of the bidding when the asking price reaches his or her valuation.
Thus, just as in the Vickrey sealed second price auction, the price paid by the buyer with the highest valuation is equal to the second highest value.
Consider then the expected payment in the sealed second-price auction.
Then the winning payment is uniformly distributed on the interval
and so the expected payment of the winner is We now argue that in the sealed first price auction the equilibrium bid of a buyer with valuation
We need to show that buyer 1's best response is to use the same strategy.
Under Vickrey's assumption of uniformly distributed values, the win probability is
In network routing, VCG mechanisms are a family of payment schemes based on the added value concept.
The basic idea of a VCG mechanism in network routing is to pay the owner of each link or node (depending on the network model) that is part of the solution, its declared cost plus its added value.
In the case of network flows, unicast or multicast, a minimum-cost flow (MCF) in graph G is calculated based on the declared costs dk of each of the links and payment is calculated as follows: Each link (or node)
This routing problem is one of the cases for which VCG is strategyproof and minimum.
In 2004, it was shown that the expected VCG overpayment of an Erdős–Rényi random graph with n nodes and edge probability p,
Prior to this result, it was known that VCG overpayment in G(n, p) is and with high probability given The most obvious generalization to multiple or divisible goods is to have all winning bidders pay the amount of the highest non-winning bid.
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 items are assigned to maximize the sum of utilities; then each bidder pays the "opportunity cost" that their presence introduces to all the other players.
A different kind of generalization is to set a reservation price—a minimum price below which the item is not sold at all.
In some cases, setting a reservation price can substantially increase the revenue of the auctioneer.
In mechanism design, the revelation principle can be viewed as a generalization of the Vickrey auction.