"l dollar bid, now 2,
now 2, will ya give me 2?
2 dollar bid, gimme 3,
gimme 3, who will gimme 3?
3 dollar bid, now 3 dollar bid,
now 4, who will ya give me 4?"

Most everyone is familiar with the light-hearted auctioneers chant, but don't let that fool you because at its core, an auction is basic method of determining the underlying economic value of an item. In fact, auctions play a major role in the world's financial markets helping to set the relative values of grains, government debts, metals, and even currencies [5]. Truly much of today's economic activity relies directly or indirectly on information derived from auctions.

Auction Types

Though there are many variations, there are four primary types of auctions, and they differ with respect to when the bidders must submit their bids and how much the auction winner must pay. Each one is discussed below:

English Auction

When most people think of an auction, the English auction is the first to come to mind; it is perhaps the most widely known auction type. As the script at the beginning of this column indicates, the bidding is moderated by an auctioneer whose job it is to keep the bidding process moving in a steady and orderly fashion. Bidding proceeds sequentially from lower bids to higher bids until eventually all the bidders drop out with the exception of the highest bidder who pays his bid price. In this system then, the person who values the item the most wins the auction and takes possession of the item. But notice that the winner is not paying his own private valuation, but rather the second highest price (that he happened to submit). English auctions are frequently used at the famous auction house Sotheby's in London.

First Price Sealed-Bid Auction

This type of auction differs significantly from the English auction where the bidding is sequential and everyone is privy to other's bids. The first price sealed bid auction proceeds with each bidder secretly writing his bid on a piece of paper. All bids are then collected at once by the auctioneer, and the person who wrote the highest bid gets the item and pays the price they wrote down. A real-life example of first price sealed-bid auctions is that of self-storage businesses. When renters abandon or default on the rent for the storage spaces, self-storage businesses usually auction off the contents of the storage spaces using first price sealed-bid auctions in an attempt to recoup some of their lost revenue from abandonment.

Second Price Sealed-Bid Auction

The second price sealed bid auction proceeds identically to the first price sealed bid auction. The only difference is that the person who wrote the highest bid gets the item but pays only the amount of the second highest bid. You may be wondering, "What kind of sense does that make?" In reality, this approach is no different than an English auction. Consider that in an English auction, the winner is the person who makes the highest bid, but the highest bid does not necessarily reflect the highest value of the winner. So in essence, the winner is paying his second-highest price. The best example of a second price sealed-bid auction is Ebay through its Proxy Bidding System [1].

Dutch Auction

The final auction type is the Dutch auction. The best way to think of a Dutch auction is that it is the reverse of an English auction. Pricing begins high (usually much higher than what anyone is likely willing to pay) and sequentially decreases until someone bids (indicates they want to buy at that price).

While Dutch auctions are less common in the US, there have been some rather well-known ones. Perhaps the best recent example of a Dutch auction was the initial public offering (IPO) of Google. Though really a variation of the Dutch auction by necessity, Google's IPO proceeded in largely the same manner. Price of the stock was gradually decreased until bidders had purchased all the shares. The price at which the shares were exhausted was referred to as the "clearing price" [3].

Winner's Curse

One interesting aspect of auctions is the Winner's Curse. The Winner's Curse is most prevelant among common (a.k.a. affiliated) values auction environments where an item's value is the same for all participants but this value is unknown. The Winner's Curse originates simply because the winner of an auction has placed the highest bid. In other words, an auction winner has placed a higher value on an item than anyone else even though in theory the value to each bidder is identical. This result makes the winner wonder if he made a mistake in determining the true value of the item. For example, during a mineral rights auction, the value of the rights is the economic value that it can generate for the owner. The winner of the auction believes the economic value of the rights is greater than what anyone else thought. So, are the rights really worth that much or was the winner overly optimistic about its economic value making the recapture of that value more difficult than originally believed? Especially with many bidders, the most likely explanation is that the bidder was overly optimistic about the potential economic profit. To avoid a winner's curse, the general principle is to lower one's private estimate of the item.

Optimal Bidding Strategies

There is extensive research literature about the best bidding strategies for each of these auctions. To simplify the discussion, let us consider the strategies for risk-neutral bidders.
English Auction: The best strategy for an English auction where bidders independently arrived at their valuations, it is best to remain an active bidder up until the point that bidding exceeds the value determined for the item. In affiliated values auctions where bidders' estimates of an object's value is both ambiguous and initially unknown to other bidders but is likely to mirror others' valuation, to avoid a winner's curse, one should revise his valuation based upon the rate and value of bids being made. In other words, use information from others' bids to update your own valuation. The update may be higher or lower.
Second Price Sealed-Bid Auction: The best strategy for this auction is to simply bid one's true valuation. The reasons for this strategy are clear. If one bids less than his valuation, then one reduces the likelihood that the bid will be successful. If one bids more than his valuation, because he pays only the second highest bid, bidding more does not result in any greater payoff. However, by bidding higher, one runs the risk that the next higher bid is higher than one's own valuation. Positive economic profit might never be realized from the item.
First Price Sealed-Bid Auction: The optimal strategy for the first price sealed-bid auction is more complicated. The theory starts from the assumption that each bidder privately determines his own valuation for the item (this assumption is known as independent values) and the values are even distributed between a high and low price. Because other bidders' valuations are private and bidders want to avoid the winner's curse, each bidder should reduce his bid price according to the formula, b = v - (v - L)/n where v is one's private valuation, L is the lowest probable valuation of the item, n is the number of bidders, and b is the resulting bid price. Notice that when the auction is competitive (n is large), the downward revision will be less and the resulting bid is closer to one's privately determined value [2].
Dutch Auction: As with the first price sealed-bid auction, the optimal strategy for this auction is to revise downward one's privately determined value estimation according to the formula presented above in order to avoid overbidding for the object.

More Auction Information

As previously mentioned, there are other auction formats and variations. The Swiss Auction, for example, is very similar to the first price sealed-bid auction. The only difference with this auction is that the winning bidder can choose whether to accept or reject the item.

While the Swiss auction is a variation, the Double Auction is an entirely different format. It works by matching bidders and sellers at agreed upon prices. Suppose a seller, among many sellers, is asking a price of $100. Further suppose that a bidder, among many bidders, is bidding $100. The bidder and seller in this case would be "matched" and the transaction would take place at that price. The pricing of bidders and sellers continues uninterrupted while new matches continue to be made. This form of auction is used at the NYSE and the AMEX stock exchanges.

Finally, the optimal bidding strategies are steeply founded in theory. In reality, bidders at an auction tend to be emotionally invested in the auction process. Especially for sealed-bid auctions where values are held in secrecy, the ambiguity of values coupled with the emotional investment in winning the auction tend to cause bidders to underestimate their chances of winning. Consequently, bidders tend to submit bids that are greater than the theoretical optimal bid amount [4].

Questions:

1) Winners Technology regularly participates in first price sealed-bid auctions for machinery. During one auction, it has determined that a laser cutting machine is worth $850,000, but it submits a bid for only $823,000. What is the likely reason for underbidding the machine?
  • a. Winners Technology is unfamiliar with the first price sealed-bid auction.
  • b. It plans on updating its bid in the next bidding round.
  • c. Winners Technology is a risk neutral bidder.
  • d. Winners Technology is a risk adverse bidder.

2) Which pairs of auctions have the same optimal bidding behavior for independent valuations?
  • a. English, Dutch
  • b. English, second price sealed-bid
  • c. First price sealed-bid, second price sealed-bid
  • d. First price sealed-bid, Dutch
  • e. Both b and d
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3) In a Dutch auction with 6 bidders, and it is likely that the highest valution is $75 and the lowest is $20, what is the optimal bidding strategy for the participant with the private valuation of $50?
  • a. $45
  • b. $75
  • c. $80
  • d. $28
  • e. $50

4) In an English auction with common valuations...
  • a. the price paid is the highest valuation among all bidders.
  • b. bidding begins at a high price and proceeds lower.
  • c. bidders may use others' bids to adjust their own valuations.
  • d. the optimal strategy for a risk neutral person is to immediately bid your highest valuation.

5) Lowering one's valuation of an auction object for the risk neutral bidder might be advisable tactic in all but which auction type?
  • a. Swiss.
  • b. English.
  • c. First price sealed-bid.
  • d. Dutch.
  • e. Second price sealed-bid.
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Answers:

1) c. Winners Technology is a risk neutral bidder following the optimal bidding strategy for a first price sealed-bid auction by lowering its valuation according to the number of bidders and what it believes the lowest valuation to be. If Winners Technology were risk adverse, it would bid higher to ensure a win. Finally, there is no second round bidding and since Winners Technology regularly attends these auctions, it is unlikely that they are unfamiliar with the auction process.

2) e. In the English and second price sealed-bid auctions, bidders focus on their true valuation. With the English auction, the bidder remains active until bidding surpasses his valuation, while in the second price sealed-bid, the bidder submits his true valuation as his bid. Conversely, in Dutch and first price sealed-bid auctions, the bidder de-rates his true valuation by an amount that depends on the number of bidders, the lowest probable valuation, and the bidder's true valuation (b = v - (v - L)/n).

3) a. Using the formula b = v - (v - L)/n, the optimal bid is $45.

4) c. Because bidders are uncertain as to the real value of the auction item, the smart bidder will update his own bid according to information gleaned from others' bids. These updates can be in the positive or negative direction. Recall, that in an English auction, the winning bid is the second highest bid and that bidding proceeds from lower to higher. Also note that bidding your highest valuation immediately may deprive you of having won the auction at a price lower than your valuation. A risk neutral person will not pursue this strategy, but a risk adverse person might.

5) e. The optimal strategy for a risk neutral bidder in a second price sealed-bid auction is to alway bid his true valuation. Lowering one's valuation and bidding less simply increases the probability that one will lose the auction. In all other auctions, lowering one's valuation and bid may be an integral part of optimal strategy and lowering the probability of the winner's curse.



References:

[1] Baye, Michael R. 2006. Managerial Economics and Business Strategy. McGraw-Hill/Irwin: New York, NY.

[2] First Price Sealed-Bid Auctions. Retrieved on 11/23/07 from http://www.econport.org/econport/request?page=man_auctions_firstpricesealed.

[3] Kuchinskas, Susan. 2004. Google Auction Imminent. Retrieved 11/23/07 from http://www.internetnews.com/bus-news/article.php/3393411.

[4] Salo, Ahtia & Weber, Martin. 1995. Ambiguity aversion in first-price sealed-bid auctions. Journal of Risk and Uncertainty, 11(2), 123-137.

[5] Tucker, Irvin B. 2006. Survey of Economics. Thomson South-Western: Mason, OH.