Why don’t we see much of VCG?
The Vickrey-Clark-Groves (VGC) procedure is a generalization of a sealed-bid second-price auction that we learned about much earlier in class. In a VCG auction, the winner of the auction is charged an amount equal to the harm that their acquisition of the item inflicts on others, where the harm is the total boost in valuation the others would get if we recomputed the optimal matching without the winning bidder. This formulation is great in theory because it makes it a dominant strategy for bidders to bid their true values, even though they know that their bids are going to be used to allocate resources.
Despite this quality, there are a limited number of real-world systems using VCG auctions (Facebook ads being a notable exception discussed in this other blog post). For example, while a VCG auction could be used as a price-setting scheme for advertisement slots in search engine queries, Google opted to use a different scheme (GSP).
While truthful bidding is a dominant strategy, there are other weaknesses of VCG auctions that could lead to their lack of use in the real world. This article discusses VCG’s vulnerability to collusion by a coalition of losing bidders and to the use of multiple bidding identities by a single bidder. It also mentions that analyses of the VCG mechanism tend to exclude the revenue granted to the original seller, which is possibly a contributing reason to Google’s decision to use a different price-setting scheme.
Additionally, this other article by researchers at the University of Waterloo notes that determining the winner of a VCG auction is often an NP-Hard problem, impacting the time it takes to find the optimal assignment when there are lots of items. The article also points out that budget constraints that prevent bidders from bidding their true values destroy the truthful bidding attribute of VCG auctions.
Overall, while the Vickrey-Clark-Gloves procedure seems to be well suited for real-life application since it makes truthful bidding a dominant strategy, the mechanisms it relies on fall apart when complexities of the real world need to be modeled as well, reducing its effectiveness.