as a uniform price auction. The uniform-price auction does not, however, result in bidders bidding their true valuations as they do in a second-price auction unless each bidder has demand for only a single unit. A generalization of the Vickrey auction that maintains the incentive to bid truthfully is known as the Vickrey–Clarke–Groves (VCG) mechanism. The idea in VCG is that items are assigned to maximize the sum of utilities; then each bidder pays the "opportunity cost" that their presence introduces to all the other players. This opportunity cost for a bidder is defined as the total bids of all the other bidders that would have won if the first bidder had not bid, minus the total bids of all the other actual winning bidders. A different kind of generalization is to set a reservation price—a minimum price below which the item is not sold at all. In some cases, setting a reservation price can substantially increase the revenue of the auctioneer. This is an example of Bayesian-optimal mechanism design. In mechanism design, the revelation principle can be viewed as a generalization of the Vickrey auction. See also Auction theory First-price sealed-bid auction VCG auction References Vijay Krishna, Auction Theory, Academic Press, 2002. Peter Cramton, Yoav Shoham, Richard Steinberg (Eds), Combinatorial Auctions, MIT Press, 2006, Chapter 1. . Paul Milgrom, Putting Auction Theory to Work, Cambridge University Press, 2004. Teck Ho, "Consumption and Production" UC Berkeley, Haas Class of 2010. Notes Types of auction