In a second-price sealed bid auction, each bidder submits a sealed bid to the seller. The high bidder wins and pays the second-highest bid for the good. The second-price auction is a special case of a Vickrey auction. As in other Vickrey auctions, it is a dominant strategy in a second-price auction for a bidder to bid their true value.
Bidding in second-price sealed-bid auctions
It can be shown that in a second-price sealed bid auction, it is a dominant strategy for a bidder to bid her true value. The argment is as follows: say there is a bidder Susie, and Susie's valuation for the item is v. Suppose the highest competing bid is p. If v is greater than p, then Susie wins the item and earns v-p if she bids her own value v. No other bids can give Susie better earning. If Susie's value v is less than p, then the best Susie can do is to bid below p and earn zero dollar. Susie earns exactly zero dollar by bidding v. Over all, to bid v is the best choice for Susie. Therefore, sometimes the second-price auction is also called demand revealing mechanism.
Comparing to the first-price sealed-bid auction and the English auction, the second-price sealed-bid auction has its comparative advantages. In an English auction, bidders' bidding strategies are severely affected by closing method. Whether the auction is run during a fixed time interval plays a key role in the auction (please see "soft close" vs "hard close"). However, in the sealed-bid auction, bidders' bidding strategies are not affected by closing method. In a first-price auction, bidders bid below their values, and therefore the first-price auction is not a demand revealing mechanism. However, as we mentioned, the second-price auction is a demand revealing mechanism.
The English auction is strategically equivalent (in theory) to the second-price auction. While the format of the English auction is quite different, it is also a dominant strategy in that format for a bidder to bid (up to) their true value before dropping out. Experimental economists have examined whether this equivalence (or isomorphism) holds in practice.
One type of cheating in the second-price sealed-bid auction is that the seller spies on the bids and then inserts a fake bid in order to increase the payment of the winning bidder. This possibility was pointed out as early as Vickrey's seminal paper that introduced this type of auction (Please see readings).
In the 1970's, U.S. Treasury Department experimented with this type of auction to sell the national debt.
W. Vickrey. Counterspeculations, auctions, and competitive sealed tenders. Journal of Finance, 16:15–27, 1961.