…sm or “the” VCG mechanism, though VCG can sometimes refer to the more general class of mechanisms). The mechanism works as follows. For every individual, we run the mechanism without her and choose the outcome that maximizes the utility of all other players given their reported types. Then we include the individual and run the mechanism again. The latter is the outcome chosen. Each player pays (or collects) the difference between the sum of utilities for the other players in the two cases. Effectively, this payment is equivalent to the individual’s social cost or benefit. Since the individual has no way of affecting the sum of utilities that occurs without her, she is effectively trying to maximize the sum of her own and everyone else’s utility. But this is exactly the same as maximizing total social utility! Aligning incentives in this way ensures not just incentive-compatibility, but also guarantees efficiency. It is also easy to find ex-post individually rational and weakly budget balanced versions of this mechanism with some pretty mild additional assumptions. We can also add arbitrary terms to the payout that the individual can’t influence (such as giving each individual some constant amount regardless of the outcome), without changing the underlying incentives. This more general set of mechanisms are called Groves Schemes, which are always dominant strategy incentive-compatible. They also happen to be the only efficient mechanisms where truth is a dominant strategy.
