Một mặt, bán đấu giá một chiều trong một thiết lập chiều duy nhất chỉ có một loại tốt để bán. Có thể có chỉ có một bản sao của mục, trong đó bán đấu giá được gọi là đơn vị duy nhất, hoặc các mục hoán đổi cho nhau nhiều, trong trường hợp bán đấu giá được gọi là nhiều đơn vị. Trong cả hai trường hợp | 162 CHAPTER 7. MECHANISM DESIGN Single-sided single-dimensional auctions In a single dimensional setting there is only one type of good for sale. There could be only one copy of the item in which the auction is called single unit or multiple interchangeable items in which case the auction is called multi-unit. In both cases in a single-dimensional auction bidders care only about the number of goods they receive and the price they pay and their bids can mention only price and in the case of multi-unit auctions quantity. The best known one-sided single-dimensional auction families are the English auction and the sealed-bid auction followed closely by the Dutch and Japanese families. Let us briefly review each of them. The English auction is perhaps the best-known family of auctions since in form or another they are used in the venerable old-guard auction houses as well as most of the online consumer auction sites. In a single-unit English auction the auctioneer sets a starting price for the good and agents then have the option to announce successive bids each of which must be higher than the previous bid usually by some minimum increment set by the auctioneer . The rules for when the auction closes vary in some instances the auction ends at a fixed time in others it ends after a fixed period during which no new bids are made in others at the latest of the two and in still other instances at the earliest of the two. The final bidder who by definition is the agent with the highest bid must purchase the good for the amount of his final bid. Multi-unit English auctions are less straightforward. For one thing they vary in the payment rules. If there are 3 items for sale the top 3 bids win one item each. In general these bids will be for different amounts the question is what each bidder should pay. In the pay-your-bid scheme the so-called discriminatory pricing rule each of the three top bidders pays a different amount namely his own bid. In the uniform pricing rule all .
