You bid, you win, you pay the amount that you bid. That's the rule for auctions, right? And that's why you want to make the lowest bid you think will win. One type of auction, though, takes the guesswork out of it with economic theory.
The Vickrey Auction isn't an alternative to the typical speed-talking, paddle-waving auction. It's an alternative to auctions in which everyone submits a sealed bid. The initial problem with auctions like these is they leave the highest bidder with a sneaking sense of dissatisfaction. Perhaps they could have bid much lower and still got their item. Who knows how low other people were willing to go?
This, in turn, leads to a bigger problem. The auction stops being about people disclosing how much they're willing to bid for an item. It becomes about them guessing the lowest bid that still gives them a chance of out-bidding their competitors. This is exactly the kind of thing the seller doesn't want. It's no picnic for the buyers either, since each one of them risks losing a item they might have won because they guessed too low.
The solution to the problem came in 1961 from William Vickrey, an economist and Nobel Laureate. He proposed that, instead of paying the price they bid, the winner would pay the price, or a small amount over the price, of the second-highest bidder.
It's not an intuitive solution, but it does work, because it removes the incentive to make a low-ball offer in order to just barely beat out everyone else. There's no need to worry if you are willing to pay a hundred dollars for, for example, a painting. If someone else is willing to pay 120, you weren't going to win anyway. If everyone else is only willing to pay 80, you just have to pay 80, or 81 dollars, and you still win. At a Vickrey Auction, everyone has an incentive to bid exactly the maximum that they are willing to pay.
The problem, and the reason Vickrey auctions aren't particularly widespread, is that they are vulnerable to people getting together to game the system with can't-lose top bids and low-ball other offers. Auctions also have two sides, and so when a seller sees that they could have gotten $100 for their item, but will have to let it go for $50, they're not pleased. So you're unlikely to find a pure Vickrey Auction in real life. If only reality were as perfect as an ideal.