There are four main types of auction:
An English auction is also known as a open ascending bid auction. This means that the bidding is open to anyone and the auctioneer raises the price until there is only one bidder left. This is the type of auction most often seen in auction houses.
It is a type of second-price auction because the winning bidder does not pay whatever they would have been willing to pay they only pay slightly above what the second highest bidder was willing to pay.
A Dutch auction is also known as an open descending price auction. This means that the auctioneer starts with a ridiculously high price that he knows no-one will ever pay and then reduces the price until someone finally bids.
This means that it is a type of first-price auction because the winning bidder pays the price that they bid and they never know what anyone else would have bid.
This type of auction is not used very often, even a company call Dutch Auction Sales doesn’t use Dutch auctions, just a normal English auction. It is seen in real life when a store gradually reduces the price of items in a sale until they finally get a buyer.
A sealed first-price auction is an auction where all the bidders submit their bids at the same time and the highest bidder wins and pays the price that they bid. It is equivalent to the Dutch auction because the highest bidder wins by paying the most they are willing to pay and they never know what others would have been willing to pay.
Finally we have a sealed second-price auction, also known as a Vickrey auction. In this type of auction the bidders bid as in a sealed first-price auction but the winning bidder pays the amount of the second highest bid. This system means that the best strategy for each bidder is to always bid their true valuation for the item.
This is similar to the system used by Google for bidding on Adwords keywords.