 Vickrey–Clarke–Groves mechanism

The pivot form chooses a reported-welfare-maximizing allocation and charges each agent the maximum welfare achievable by the others without that agent minus the others' welfare in the chosen allocation. With quasilinear utility, truthful reporting is a dominant strategy because the first term in the payment depends only on other reports. For two identical items and three unit-demand bidders, each winner pays the lowest reported valuation and the loser pays zero.

The Vickrey–Clarke–Groves (VCG) mechanism is a type of auction and mechanism design theory that encourages truthful bidding from participants in a public goods setting. It is named after three economists: William Vickrey, Edward Clarke, and Theodore Groves, who contributed to the underlying principles of this mechanism.