Dutch Auctions by Tyler Jones

Here is my canned response on Dutch Auctions. If you need more information, please let me know, giving details about the problem at hand.

A Dutch Auction is an auction format on eBay wherein a seller has a large number of identical items that she wishes to sell. Rather than running 50 or more separate auctions, she runs one auction and sells all 50 of them there.

Each buyer enters a bid containing two parts: The number of items he wants and the price per item he is willing to pay. In Dutch Auctions, there are no proxies or max bids. Each bid is recorded in full in the bid history. When bidding, note that you do not always have to be the highest bidder. You only have to bid high enough so that the total number of items bid by bidders higher than you does not exceed the total number of items. Very often, people bid under the current high bidder and still qualify.

When the auction is over, there may be one winner or multiple winners. The bids are sorted in descending order of the per-item price. The highest bidder wins the number of items he bid on, and so on down the line. From the highest bidder down, each bidder wins the number of items that he bid on until the number of items in the auction is expended.

Each bidder pays the same price per item. This is the per item price of the lowest winning bidder. It's very possible that if you win a Dutch Auction, you will likely pay an amount less than what you bid. If the total number of items bid on by the bidders is less than the number of items in the auction, the all winners will pay the opening price, even if all bidders bid more than that.

I was under the impression that if the total number of items bid upon EQUALLED the total number of items in the auction, then the per item price would also be equal to the opening bid, but recent auctions have shown that theory incorrect. If the number of items bid upon equals the number of items available, then the per item price will be equal to the per item bid of the lowest bidder.

Given the mathematics, the lowest winning bidder in a Dutch Auction (I don't know if there's an official term for this) might "win" fewer items than she bid on. If this happens, you are NOT obligated to buy the so-called "partial quantity". Sellers, however, are obligated to sell to you in this case. Even if the low winner does not complete the transaction, that does not affect the per item price that everybody else pays.

Re-bidding in a Dutch Auction is slightly different than in a normal auction. Each bid that you make cancels any previous bids that you made before. It's not a simple additive proxy like in a regular auction. The number of items are not additive either. For example, if you bid on 2 items, then come back a day later and bid on 3, you are only bidding on 3 items, not 5. Dutch Auction bids are goverened by the equation

"c = i * p"

Where "i" is the number of items that you want, "p" is the price per item, and "c" is the total cost of your bid. Each time that you re-bid, "c" must increase. You can always bid on more items for a higher price per item. Bidding on more items for less money per item or fewer items for a higher price per item is possible. Whip out your calculator and confirm that with the new bid, the total cost is greater than the old cost. Urban Legends tell me that the most common reasons for re-bidding are to bid a higher price for the same number of items, or to bid on more items at a lower price, possibly to decrease your per-unit cost for a re-sale.

Obviously, you cannot bid on fewer items for a lower price per item. In that case, there is no way that "c" can ever increase. And for you math geeks, no, you can't enter negative, imaginary or complex numbers for your bids, so please don't send me e-mails with "proof" that i and p can both decrease and result in a increased "c". :-)

You cannot have an auction that is both Dutch and Reserve Price. You can have one, or the other, or neither, but not both.

Several eBay users have come up with some very unusual "what if" scenarios regarding Dutch Auctions that are not covered in the rules. I can guess what the answers are, but they should be dealt with a case by base basis through eBay.