2018년 2월 22일 목요일

발췌: 경매이론, Lucking-Reiley // Vickrey Auctions in Practice (2000)


출처: David Lucking-Reiley 지음. "Vickrey Auctions in Practice: From Nineteenth Century Philately to Twenty-first Century E-commerce," Journal of Economic Perspective, Apr 2000.

* * *

※ 발췌 (excerpt):

In his seminal work on auction theory, William Vickrey (1961) pointed out three types of auctions used in practice: the English ascending-bid auction, the (first-price) sealed-bid auction, and the Dutch declinging-price auction. He first compared the sealed-bid auction, in which all bidders submit sealed bids and the highest bidder wins at his bid price, to the Dutch auction, in which prices are called out in a descending order until a bidder claims the item at the current price.

Applying game theory to the study of auctions, Vickrey showed that these two auctions are strategically equivalent; that is, a bidder in the Dutch auction should wait until the price falls to the exact amount she would bid if she had been participating in a sealed-bid auction. He also showed how to compute Nash equilibrium bid strategies for bidders; in both the sealed-bid and Dutch auction formats, each bidder should bid strictly less than her maximum willingness to pay for the good. ( ... ... )

Next, Vickrey considered the well-known English ascending-price auction, in which bidders raise each other bids until only bidder remains.
  • Vickrey showed that in this type of auction, each bidder's dominant strategy is to keep bidding until the price reaches her maximum willingness to pay for the good, and then to drop out of the auction. 
  • The highest-value bidder then ends up winning the good, and paying a price equal to the second-highest bidder's value (plus one bid increment, to guarantee victory). 
This equilibrium differs from those of the Dutch and sealed-bid auction formats: the optimal strategy for a bidder is to reveal her full value for the good (except for the winner, who wins before the auction actually reaches her dropout price), rather than bidding strictly less than her value. Optimal bidding in the English auction is simpler and more robust because it involves dominant strategies: that is, one's optimal bidding strategy does not depend on the bids submitted by one's rivals.
Vickrey then asked whether there existed a sealed-bid procedure that would be strategically equivalent to the English ascending-price auction, in the way that the standard first-price sealed-bid auction was equivalent to the Dutch descending-price auction. He answered in the affirmative, proposeing the rules for a "second-price" sealed-bid auction (so named to distinguish it from the standard "first-price" sealed-bid auction) in which each bidder would again have a dominant strategy to bid equal to her own value. As Vickrey wrote: "It is easily shown that the required procedure is to ask for bids on the understanding that the award will be made to the highest bidder, but on the basis of the price set by the second highest bidder."

This second-price sealed-bid auction is frequently called the "Vickrey auction" by economists. Indeed, the economics profession has generally credited Vickrey with being the first to propose this auction format ( ... ... ). There seemed to be no examples of a second-price sealed-bid auction occurring prior to Vickrey's 1961 article. In the article, Vickrey discusses the use of the English auction as a standard auction format for various types of goods, the use of the Dutch auction in selling flowers in the Netherlands, and the use of first-price sealed-bid auction for sales of real estate and securities, but nowhere does he indicate that a second-price sealed-bid auction had ever been used. Similarly, an extensive survey of the various types of bidding procedures in practice, by Cassady (1967), makes no mention of the second-price sealed-bid auction.

( ... ... ) [Rothkoph, Teisberg, and Kahn (1990)] also present some examples from the last few decades which are similar in flavor to the Vickrey format: uniform-price auctions of Treasury bills and other securities (that is, the bills are all sold at one price, not at the prices bid by the highest bidders); certain proposed auctions for electric power generation; and stamp auctions, which I will focus on this paper. Rothkoph, Teisberg, and Kahn note: "In some auctions of collectible items such as stamps and autographs, the auction involves mailed-in sealed bids based on a catalogu listing as well as oral bids," and that winning mail bidders pay one bid increment higher than the second-highest bid received.[주]1
[주]1. Thiel and Petry (1995) perform a test of auction theory based on similar stamp auctions. They use an interesting and original data set of bids submitted by mail bidders in stamp auctions from 1923 to 1937. They characterize these auctions as "second-price," recognizing the equivalence discussed in this paper, though their auctions include an English bidding floor in addition to the mail bids.

It turns out that the Vickrey auction has actually been used more often than previously thought. ( ... ... ) I came across a website for the company Antebellum Covers, which advertised an auction by mail for Civil War memorabilia. I was intrigued to read that the auction used the second-price sealed-bid rule. I contacted the auctioneer to ask how he came to use this rule, and he replied that it was a standard procedure that had been going on for years in the market for paper collectibles, from Civil War soldiers' letters to postage stamps. As I investigated further, I found that auctioneers in the stamp market had utilized the second-price sealed-bid auction. In fact, several hundred auctioneers used the pure Vickrey auction, accepting no oral bids whatsoever, as their primary method of business before Vickrey ever wrote his 1961 artice--some even before Vickrey was born! [주]2
[주]2. Moldovanu and Tietzel (1998) have discovered an even earlier example of a second-price-type mechanism, designed by Goethe in 1797. Goethe's procedure was to pit a single bidder (a publisher) against a secret reserve price, to get the publisher to reveal his true willingness to pay for the manuscript. Unfortunately, Goethe's agent failed to carry out the procedure correctly.

( ... ... )


Precursors to the Vickrey Auction: The Stamp Auctions of the 1870s

The first adhesive postage stampt(the "Penny Black") appeared in England in 1840; the first U.S. postage stamd was issued in 1847; and the hobby of stamp collecting began in earnest in the 1850s. The first stamp auctions took place from 1870 to 1882, most of them in New York City. In the 1890s, such auctions became common, with over 2,000 auctions held worldwide by 1900.[주]3

These auctions generally used conventional English ascending-price auction rules. However, from the earliest years, accommodations were made to individuals who wished to bid without having to travel to the auction in person. The first auction catalogue of stamp dealer William P. Brown, New York Cit, 1878, reads as follows:

That out-of-town collectors may have equal facilities for purchasing with city collectors, bids may be sent to the auctioneers, Messrs. Bangs & Co., or to William Erving, P.O. Box 3222, N.Y. City, who will either of them represent their bids the same as though they were personally present, and without charge. Thus, supposing either of these parties receives two bids on one lot of 20 and 25 cents apiece, they would start the lot at 21 cents, at which price it would be given to the person sending the 25 cent order, unless some one present advanced, when they would continue to bid, stopping at the limit of 25 cents. Collectors can safely entrust these parties with their bids as strictly confidential, and we trust they will find it more satisfactory than paying the usual dealers' commission of ten per cent for purchasing. Persons sending bids should give the number of the lots and the highest price they are willing to give, when the lot will be bought for them as low as possible consistent with the representation of other bids.

The phrase "usual dealers' commission" refers to the fact that quite a few other stamp auctions had previously offered a "mail bid" service, charging a fee of 10 percent to serve as the bidder's agent on the auction floor. Brown appears to be the first to have waived this fee, with the intentin of treating mail bidders exactly the same as floor bidders. The practice is common at many auction houses today, not just with stamps, but also in auctions of wine, art, and other collectibles. Clearly, this absentee bidding anticipates the Vickrey auction in both spirit and effect, because it results in the absent bidder's price being determined by the second-highest bid.

The 1870s also saw the beginning of "mail sales" in the stamp market: sales with no floor bids, but only sealed bids submitted through the mail.[주]4 The first such sales, held around 1877, were "tender sales," or what economist today would call first-price sealed-bid auctions. ( ... ... )


Vickrey Auctions for Stamps: From 1893 to the Present

A Vickrey auction is a natural extension of the two precursors discussed above. Certain standard auctions allowed absetee bidders to submit maximum bid amounts, and awarded goods to winning absetee bids at the price of one increment over the second-highest bid. Other sales accepted only sealed bids, but the winner paid the highest price bid. The Vickrey auction combines these two ideas: a sealed-bid-only sale that awards the goods at the price of one bid increment over the second-highest bid.

The earliest Vickery auction I have been able to identify was held by Wainwright & Lewis, of Northampton, Massachusetts, in 1893. Their sale announcement, published in the stamp journal ^Golden Star^ in March 1893, reads as follows:

Catalogue of a Collection of U.S. and Foreign Stamps

To be sold WITHOUT RESERVE except where noted.
Bids will be received up to 4 P.M., May 15, 1893.
Bids are for the LOT, and, contrary to the usual custom in sales of this kind, we shall make this a genuine AUCTION sale; that is to say, each lot will be sold at an advance of from 1c to 10c above the second highest bidder. Address all bids to

Wainrights & Lewis, Northampton, Mass.

The phrase "an advance of from 1c to 10c above the second highest bidder" indicates that the final price would be one minimum bid increment above the second-highest bid. In calling this a "genuine AUCTION sale," Wainwright & Lewis are indicating their recognition that "selling at one advance over the second highest bid" is the key feature of a standard English ascending-price auction (as contrasted with the "usual" sealed-bid sale, which used a first-price rule).

Wainwright & Lewis appear to have held no further auctions, but the same concept was  used by others. In 1897, the pioneering stamp dealer William P. Brown of New York, earlier noted as the first to offer no-fee mail bids, became the first major stamp dealer to hold a Vickrey auction, with his Auction Sale No. 2. The Terms of Sale listed in the catalog describe the public reserve prices used in the auction (referred to as the dealer's own offer to buy), the minimum bid increments ( ... ... ), shipping arrangements, and the following description of the pricing rule:

These goods are not sold publicly to those who come in person, but those who send or hand us their offers, which are confidential until after the sale. The highest offer secures the purchase.

... At the time appointed for the sale all the offers received will be examined and awarded to the highest competitor. For instance we will suppose lot No 2006 has on it our offer of $1.50; and we find three others, one for $1.60, one for $2, and one for $10.00. The $10.00 offer receives it for #2.10, which is the lowest price at which he could obtain it if all the competitors were present.

The Vickrey auction format spread gradually to other stamp dealers. Several companies established long-running businesses based on Vickre-style "mail sales," including ( ... ... ). Most of these companies had started out with first-price sealed-bid auction rules, but switched to second-price rules at the date indicated.

Through 1920, such "mail sales" remained small relative to the conventional English auction business in stamps, in terms of both price and quantity. Even among the mail sales, Vickrey auctions remained less common than first-price sealed-bid auctions. However, some of the Vickrey-style auctioneers took great care to explain the benefits of their auction format to their bidders. Toledo Stamd Company, for ex., wrote in its 15th Mail Auction Sale catalog in 1907:

To those who have never bid on Auction Sales before we wish to say that this is one of the best ways to add to your collection of stamps that you would not be able to purchase at the price otherwise. You say just how much you wish to pay for a lot, and if no one else has overbid you, you get the stamps. If your bid is too high we buy for you a small advance over the next highest bid, so you are protected in any case.

( ... ... )

From the 1930s to the present, the majority of mail sales of stamps have used the Vickrey second-price rule. The rule became so standard that it no longer had to be explained. For example, in 1935 the Belmont Stamp Company of Dallas, Texas (appropriately enough, located on "Vickery [sic] Blvd."!) stated the rule in its First Mail Auction as follows: "All lots will be sold to the highest bidder at a slight advance over the next highest bid."  Nearly  identical language can be found  in numerous other mail-sale catalogs from the 1930s to the present. In other cases, the price rule is even less explicitly stated. For example, several catalogs tell the bidder that "in submitting your bids, you understand that we will purchase the items for you at the lowest price possible."

On the basis of his collection of stamp sale catalogues, Dr. Trenchard estimates that at least several hundred different stamp companies ran second-price auctions by mail prior to the publication of Vickrey's paper in 1961.


The Future of the Vickrey Auction

Despite the attractive theoretical properties of the Vickrey auction format and its prominence in the stamp busiess, it is rare in the economy. Rothkopf, Teisberg, and Kahn (1990) propse two explanations for the scarcity of Vickrey auctions: 1) bidders may fear truthful revelation of information to third parties with whom they interact after the auction; and 2) bidders may fear auctioneer cheating. ( ... ... )

In the course of my research on stamp auctions, I have found that bidders do fear auctioneer cheating in second-price auctions. Once you have submitted your maximum willingness to pay, the auctioneer has an incentive to cheat, and pretend that another bid was received just under your maximum amount.

Dr. Trenchard, a longtime participant in stamp auctions and mail sales, indicates that he is reluctant to reveal his true willingness to pay in a Vickrey auction. "Unless I have confidence in the company," he writes, "I will not send any mail bids. And it's risky to send an outlandishly high mail bid, because you alert [the auctioneer] to information you don't want him to have. For mail sales, I try to make more conservative bids." He expresses the same wariness of mail bids sent to an auctioneer for a floor auction: "Never send a mail bid to an auctioneer. If you give him an outlandish bid, he'll wonder why, look at the lot and perhaps discover what I know that he didn't know. He can then withrow it!"

Of course, a bidder doesn't face this problem when attending an English ascending-price auction, since there is no need for the winner to reveal how high he would have been willing to bid. ( ... ... )

댓글 쓰기