Auctions

William Vickrey first established the taxonomy of auctions based on the order in which the auctioneer quotes prices and the bidders tender their bids. He established four major (one-sided) auction types: (1) the ascending-bid (open, oral, or English) auction; (2) the descending-bid (Dutch) auction; (3) the first-price, sealed-bid auction; and (4) the second-price, sealed-bid (Vickrey) auction.

The most common type of auction, the English auction, is often used to sell art, wine, antiques, and other goods. In it, the auctioneer opens the bidding at a reserve price (which may be zero), the lowest price he is willing to accept for the item. Once a bidder has announced interest at that price, the auctioneer solicits further bids, usually raising the price by a predetermined bid increment. This continues until no one is willing to increase the bid any further, at which point the auction is closed and the final bidder receives the item at his bid price. Because the winner pays his bid, this type of auction is known as a first-price auction.

The Dutch auction, also a first-price auction, is descending. That is, the auctioneer begins at a high price, higher than he believes the item will fetch, then decreases the price until a bidder finally calls out, “Mine!” The bidder then receives the item at the price at which he made the call. If multiple items are offered, the process continues until all items are sold. One of the primary advantages of Dutch auctions is speed. Since there are never more bids than there are items being auctioned, the process takes relatively little time. This is one reason they are used in places such as flower markets in Holland (hence the name “Dutch”).

In the English and Dutch auctions, bidders receive information as others bid (or refrain from bidding). However, in the third type of auction, known as the first-price, sealed-bid auction, this is not the case. In this mechanism, each bidder submits a single bid in a sealed envelope. Then, all of the envelopes are opened and the highest bidder is announced, and he receives the item at his bid price. This type of auction is most often used for refinancing credit and foreign exchange, among other (primarily financial) venues.

The fourth type is the second-price, sealed-bid auction, otherwise known as the Vickrey auction. As in the first-price, sealed-bid auction, bidders submit sealed envelopes in one round of bid submission. The highest bidder wins the item, but at the price offered by the second-highest bidder (or, in a multiple-item case, the highest unsuccessful bid). This type of auction is rarely used aside from setting the foreign exchange rates in some African countries.

One might think so many canonical auction forms unnecessary, that there is always a best choice that will yield the most surplus to the seller. In fact, under some strict assumptions, the revenue equivalence theorem (also due to Vickrey) states that all four auction types will result in an identical level of revenue to the seller. However, these assumptions regarding the nature of the item’s value and the risk attitudes of the bidders are very restrictive and rarely hold.

The first assumption of the theorem is that the asset being auctioned has an independent, private value to all bidders. This assumption tends to hold when the item is for personal consumption, without thought toward resale, as might be the case for furniture, art, or wine. In this case, the value of the item is considered to be personal and independent of the value others might place on it (independent, private values). The assumption does not hold when bidders perceive a value of resale, either of the item itself or of a by-product of the item. Buying land for the rights to the oil that lies beneath it would be a good example. In this case, the value is common; that is, individual bids are predicated not only on personal valuation, but also on the valuation of prospective buyers. Each bidder tries to estimate the value of an object using the same known measurements (common values), but their conclusions may vary widely.

In common-value environments, bidders may face the “winner’s curse.” If all of the bidders will eventually realize the same value from the item, then the primary differentiator between the bidders is their perception of that value. Absent special information about the item being purchased, the winner is the person with the largest positive error in his valuation, and, unless he is lucky, he will wind up losing money.

The second assumption of the revenue equivalence theorem is that all bidders are risk-neutral. The strict definition of risk neutrality is: given the choice between a guaranteed return r and a gamble with expected return also equal to r, the bidder is completely indifferent. The bidder who prefers the guaranteed return is said to be “risk-averse,” while the bidder who prefers the gamble is said to be “risk-loving.”

The style of auction a seller chooses depends on his judgment about which of these assumptions holds. If values are common rather than independent, the English auction yields higher seller revenue than the second-price, sealed-bid auction, which in turn yields higher revenues than the Dutch and first-price, sealed-bid auctions (which are tied). The rankings illustrate the strategic advantages of increased information. Because the English auction reveals all bids to all bidders, it permits dynamic updating of personal valuation. (If I see that others believe the real estate is worth more, I too may decide it is worth more.) In comparison, bidders, recognizing the winner’s curse, bid less aggressively in first-price, sealed-bid auctions and shade their bids downward. Similar reasoning applies to Dutch (descending) auctions. While the information is not updated in a second-price sealed-bid format, the winner pays the bid of the next-highest bidder, and so bidders raise bids, secure that they will not be disadvantaged if rival bids are lower.

In fact, in both the first-price, sealed-bid auction and the Dutch auction, no information is revealed and the bidder pays the value of his bid. Therefore, in terms of revenue maximization, it does not matter which of these auctions a seller chooses; nor does it matter whether the bidders have private or common values.

What about the role of risk aversion? In first-price, sealed-bid and Dutch auctions, risk aversion causes bidders to bid slightly higher than they might otherwise. Since they have only one chance to bid, fear of losing the item induces overbidding. In the English and Vickrey auctions, however, bidders are induced to bid their true valuation, regardless of risk attitudes.

Once a seller has decided on which of the four basic auction forms to use, he can use many variations within the auction to further manipulate the outcome to maximize revenue. These mechanisms can have profound, and often counterintuitive, effects on bidding behavior—and therefore on outcomes. Among the available mechanisms are reserve prices, entry fees, invited bidders only, closing rules, lot sizes, proxy bidding, bidding increment rules, and postwin payment rules.

The 1994 U.S. Federal Communications Commission (FCC) auctions of wireless bandwidth provide a useful example of both the successes and the failures of auction design. The auction to allocate Personal Communications Service (PCS) spectrum had four primary goals: (1) to attain efficient allocation of spectrum, (2) to encourage rapid deployment and network build out, (3) to attain diversity of ownership, and (4) to raise revenue. Goals 1, 2, and 4 are met by any well-designed auction, as the winner is the one who values the item most. PCS licenses are a classic common-values good, in that they have a common, large, but uncertain value, triggering the winner’s curse.

The FCC developed an elaborate network of rules to ensure the desired outcomes. To encourage price discovery, the auction was a multiround, ascending-bid, first-price auction. The many licenses available covered the entire United States, allowing major complementarities and substitutes in this market. To allow bidding that took this into account, the auctions were simultaneous, and no auction ended until they all did (every license was open until there were no more bids on any of them). Further, because the FCC wanted to discourage bidders from sitting on the sidelines until the very end, an activity rule was imposed. These and an elaborate network of other rules were carefully balanced to ensure the desired outcome. The result was great success in maximizing revenues.

The 1994 FCC auction stumbled, however, in its goal of diversifying ownership. To achieve this goal, the FCC set aside two blocks (C and F) for entrepreneurs, female and minority-owned firms, and regional companies. To that end, the FCC took the carefully designed auction and changed it just a little bit.

Bidders in these two special blocks received a 25 percent bid credit. That is, if they bid eighty dollars for an item, the bid was treated as if they had bid one hundred dollars. Further, their deposit requirement was just one-fifth of what the other winning bidders paid. Lastly, “diversity bids” were offered a generous installment payment plan. Bidders had a month to furnish 10 percent of the bid and owed no more principal until seven years later. The interest for this loan was charged at the T-bill rate. Unfortunately, this seemingly small change had disastrous effects.

The payment policy created moral hazard (see insurance) by, in effect, providing bidders with low-cost insurance against big misestimates or drops in the value of the bandwidth. Since winning bidders had to make a down payment of only 10 percent, if, after seven years, the item turned out to be worth less than 90 percent of the bid price, then the purchaser could simply default. This is precisely what happened. Companies bought the licenses and invested 10 percent, and then declared bankruptcy when the license turned out to be worth less than 90 percent of the bid. Nearly every company that won a license in the C or F blocks in the 1994 auction either went bankrupt or was bought by a larger firm. In the end, the FCC’s ham-fisted pursuit of a noble goal destroyed this segment of the auction entirely. PCS auctions continue today, though they have been massively restructured.