Vickrey–Clarke–Groves auction

In auction theory, a Vickrey–Clarke–Groves (VCG) auction is a type of sealed-bid auction of multiple items. Bidders submit bids that report their valuations for the items, without knowing the bids of the other people in the auction. The auction system assigns the items in a socially optimal manner: it charges each individual the harm they cause to other bidders. It also gives bidders an incentive to bid their true valuations, by ensuring that the optimal strategy for each bidder is to bid their true valuations of the items. It is a generalization of a Vickrey auction for multiple items.

The auction is named after William Vickrey,Edward H. Clarke, and Theodore Groves for their papers that successively generalized the idea.

Formal description

For any set of auctioned items and any set of bidders , let be the social value of the VCG auction for a given bid-combination. For a bidder and item , let the bidder's bid for the item be . The notation means the set of elements of A which are not elements of B.