Auctions

In this section, we examine auction markets—markets in which products are bought and sold through formal bidding processes.19 Auctions come in all sizes and shapes. They are often used for differentiated products, especially unique items such as art, antiques, and the rights to extract oil from a piece of land. In recent years, for example, the U.S. Treasury has relied on auctions to sell Treasury bills, the Federal Communications Commission has used auctions for the sale of portions of the electromagnetic spectrum for cellular telephone services, the International Olympic Committee has auctioned television rights, and the Department of Defense has used auctions to procure military equip- ment. Auctions like these have important advantages: They are likely to be less time-consuming than one-on-one bargaining, and they encourage competition among buyers in a way that increases the seller ’s revenue.

Why have auctions become so popular and so successful? The low cost of transacting is only part of the answer. Unlike sales in retail stores, auctions are inherently interactive, with many buyers competing to obtain an item of inter- est. This interaction can be particularly valuable for the sale of items such as artwork or sports memorabilia that are unique, and therefore do not have estab- lished market values. It can also be helpful for the sale of items that are not unique but whose value fluctuates over time.

An example is the daily auctioning of fresh tuna at a Tokyo fish market.20 Each tuna is unique in size, shape, and quality, and consequently in value. If each transaction were carried out through rounds of bargaining and negotiation with potential buyers, it would be extremely time-consuming. Instead, sales occur every morning by means of an auction in which each tuna is sold to the

highest bidder. This format creates large savings in transaction costs and thereby increases the efficiency of the market.

The design of an auction, which involves choosing the rules under which it operates, greatly affects its outcome. A seller will usually want an auction for-mat that maximizes the revenue from the sale of the product. On the other hand, a buyer collecting bids from a group of potential sellers will want an auction that minimizes the expected cost of the product.

1. Auction Formats

We will see that the choice of auction format can affect the seller ’s auction rev- enue. Several different kinds of auction formats are widely used:

  1. English (or oral) auction: The seller actively solicits progressively higher bids from a group of potential buyers. At each point, all participants are aware of the current high bid. The auction stops when no bidder is willing to surpass the current high bid; the item is then sold to the highest bidder at a price equal to the amount of the high bid.
  2. Dutch auction The seller begins by offering the item at a relatively high price. If no potential buyer agrees to that price, the seller reduces the price by fixed amounts. The first buyer who accepts an offered price can buy the item at that price.
  3. Sealed-bid auction All bids are made simultaneously in sealed envelopes, and the winning bidder is the individual who has submitted the highest bid. The price paid by the winning bidder will vary, however, depending on the rules of the auction. In a first-price auction, the sales price is equal to the highest bid. In a second-price auction, the sales price is equal to the second-highest bid.

2. Valuation and Information

Suppose you want to sell a distinctive and valuable product such as a painting or a rare coin. Which type of auction is best for you? The answer depends on the preferences of the bidders and the information available to them. We consider two cases:

  1. In private-value auctions each bidder knows his or her individual valu- ation or reservation price, and valuations differ from bidder to bidder. In addition, each bidder is uncertain about the value that other bidders place on the product. For example, I might value a signed Barry Bonds home run baseball very highly but not know that you value it less highly.
  2. In common-value auctions, the item to be auctioned has approximately the same value to all bidders. Bidders, however, do not know precisely what that value is—they can only estimate it, and bidders’ estimates will vary. For example, in an auction of an offshore oil reserve, the value of the reserve is the price of oil minus the extraction cost, times the amount of oil in the reserve. As a result, the value should be about the same for all bid- ders. However, bidders will not know the amount of oil or the extraction cost—they can only estimate these numbers. Because their estimates will differ, they might bid very different amounts to get the reserve.

In reality, auctions can have both private-value and common-value ele- ments. In the oil reserve auction, for example, there may be some private-value elements because different oil reserves may entail different extraction costs. However, to simplify matters we will separate the two. We begin our discussion with private-value auctions and then move on to common-value auctions.

3. Private-Value Auctions

In private-value auctions, bidders have different reservation prices for the offered item. We might suppose, for example, that in an auction for a signed Barry Bonds baseball, individuals’ reservation prices range from $1 (someone who doesn’t like baseball but is bidding just for fun) to $600 (a San Francisco Giants fan). Of course, if you are bidding for the baseball, you don’t know how many people will bid against you or what their bids will be.

Whatever the auction format, each bidder must choose his or her bidding strategy. For an open English auction, this strategy is a choice of a price at which to stop bidding. For a Dutch auction, the strategy is the price at which the indi- vidual expects to make his or her only bid. For a sealed-bid auction, the strategy is the choice of bid to place in a sealed envelope.

What are the payoffs in this bidding game? The payoff for winning is the dif- ference between the winner ’s reservation price and the price paid; the payoff for losing is zero. Given these payoffs, let’s examine bidding strategies and out- comes for different auction formats.

We will begin by showing that English oral auctions and second-price sealed-bid auctions generate nearly identical outcomes. Let’s begin with the second-price sealed-bid auction. In this auction, bidding truthfully is a dominant strategy—there is no advantage to bidding below your reservation price. Why? Because the price you pay is based on the valuation of the second highest bid- der, not on your own valuation. Suppose that your reservation price is $100. If you bid below your reservation price—say, $80—you risk losing to the second- highest bidder, who bids $85, when winning (at, say, $87) would have given you a positive payoff. If you bid above your reservation price—say $105—you risk winning but receiving a negative payoff.

Similarly, in an English auction the dominant strategy is to continue bidding until the second person is unwilling to make a bid. Then the winning bid will be approximately equal to the reservation price of the second person. In any case, you should stop bidding when the bidding reaches your reservation price. Why? Because if you stop bidding at a point below your reservation price, you risk losing a positive payoff; if you continue beyond your reservation price, you will be guaranteed a negative payoff. How high will the bidding go? It will con- tinue until the winning bid is approximately equal to the reservation price of the second-highest bidder. Likewise, in the sealed-bid auction the winning bid will equal the reservation price of the second-highest bidder. Thus, both auction formats generate nearly identical outcomes. (The outcomes should differ in the- ory only by a dollar or two.) To illustrate, suppose that there are three bidders whose valuations are $50, $40, and $30, respectively, and furthermore the auc- tioneer and the bidders have complete information about these valuations. In an English auction, if your valuation was $50 you would offer a winning bid of $40.01 in order to win the bidding from the individual whose reservation price was $40.00. You would make the identical bid in a sealed-bid auction.

Even in a world of incomplete information, we would expect similar results. Indeed, you know that as a seller, you should be indifferent between an oral English auction and a second-price sealed-bid auction, because bid- ders in each case have private values. Suppose that you plan to sell an item using a sealed-bid auction. Which should you choose, a first-price or a second- price auction? You might think that the first-price auction is better because the payment is given by the highest rather than the second-highest bid. Bidders, however, are aware of this reasoning and will alter their bidding strategies accordingly: They will bid less in anticipation of paying the winning bid if they are successful.

The second-price sealed-bid auction generates revenue equal to the second- highest reservation price. However, the revenue implications of a first-price sealed-bid auction for the seller are more complicated because the optimal strat- egy of bidders is more complex. The best strategy is to choose a bid that you believe will be equal to or slightly above the reservation price of the individual with the second-highest reservation price.21 Why? Because the winner must pay his or her bid, and it is never worth paying more than the second-highest reser- vation price. Thus, we see that the first-price and second-price sealed-bid auc- tions generate the same expected revenue.

4. CommonValue  Auctions

Suppose that you and four other people participate in an oral auction to pur- chase a large jar of pennies, which will go to the winning bidder at a price equal to the highest bid. Each bidder can examine the jar but cannot open it and count the pennies. Once you have estimated the number of pennies in the jar, what is your optimal bidding strategy? This is a classic common-value auction, because the jar of pennies has the same value for all bidders. The problem for you and other bidders is the fact that the value is unknown.

You might be tempted to do what many novices would do in this situation— bid up to your own estimate of the number of pennies in the jar, and no higher. This, however, is not the best way to bid. Remember that neither you nor the other bidders knows the number of pennies for certain. All of you have inde- pendently made estimates of the number, and those estimates are subject to error—some will be too high and some too low. Who, then, will be the winning bidder? If each bidder bids up to his or her estimate, the winning bidder is likely to be the person with the largest positive error—i.e., the person with the largest overes- timate of the number of pennies.

THE WINNER’S CURSE To appreciate this possibility, suppose that there are actually 620 pennies in the jar. Let’s say the bidders’ estimates are 540, 590, 615, 650, and 690. Finally, suppose that you are the bidder whose estimate is 690 and that you win the auction with a bid of $6.80. Should you be happy about winning? No—you will have paid $6.80 for $6.20 worth of pennies. You will have fallen prey to the winner’s curse: The winner of a common-value auction is often worse off than those who did not win because the winner was overly optimistic and, as a consequence, bid more for the item than it was actually worth.

The winner ’s curse can arise in any common-value auction, and bidders often fail to take it into account. Suppose, for example, that your house needs to be painted. You ask five companies to give you cost estimates for the job, telling each that you will accept the lowest estimate. Who will win the job? It will prob- ably be the painter who has most seriously underestimated the amount of work involved. At first, that painter might be happy to have won the job, only later to realize that much more work is required than was anticipated. The same prob- lem can arise for oil companies bidding for offshore oil reserves when the size of the reserve and cost of extraction are uncertain (so that the value of the reserve is uncertain). Unless the companies take the winner ’s curse into account, the win- ning bidder is likely to win by overestimating the value of the reserve and will thus pay more than the reserve is worth.

How should you take the winner ’s curse into account when bidding for an item in a common-value auction? You must not only estimate the value of the item that you are bidding for, but also account for the fact that your estimate— and the estimates of the other bidders—are subject to error. To avoid the win- ner ’s curse, you must reduce your maximum bid below your value estimate by an amount equal to the expected error of the winning bidder. The more precise your estimate, the less you need to reduce your bid. If you can’t assess the pre- cision of your estimate directly, you can estimate the variation in the estimates of the other bidders. If there is a lot of disagreement among these bidders, it is likely that your estimate will be similarly imprecise. To measure the variation in bids, you can use the standard deviation of the estimates, which can be calcu- lated using statistical methods.

Oil companies have been bidding for oil reserves for years, and thus are able to estimate this standard deviation quite well. They can thereby take the win- ner ’s curse into account by reducing their maximum bids below their value estimates by an amount equal to the expected error of the winning bidder. As a result, oil companies rarely feel they have made a mistake after winning an auction. House painters, on the other hand, are often less sophisticated in their bidding decisions and suffer from the winner ’s curse.

The winner ’s curse is more likely to be a problem in a sealed-bid auction than in a traditional English auction. In a traditional auction, if you are the only bidder who is overly optimistic, you can still win the bidding by offering only slightly more than the second-highest bidder. Therefore, for the winner ’s curse to be a problem, at least two bidders must be overly optimistic. By contrast, in a sealed-bid auction, your optimism could encourage you to outbid everyone else by a substantial margin.

5. Maximizing Auction Revenue

Now let’s return to the question of auction design from the viewpoint of the seller. Here are some useful tips for choosing the best auction format.

  1. In a private-value auction, you should encourage as many bidders as pos- sible: Additional bidders increase the expected bid of the winner and the expected valuation of the second-highest bidder as well.
  1. In a common-value auction, you should (a) use an open rather than a sealed- bid auction because, as a general rule, an English (open) common-value auction will generate greater expected revenue than a sealed-bid auction; and (b) reveal information about the true value of the object being auc- tioned, thereby reducing concern about the winner ’s curse and, conse- quently, encouraging more bidding.
  2. In a private-value auction, set a minimum bid equal to or even some- what higher than the value to you of keeping the good for future This will protect against a loss if there are relatively few bidders who do not value the good very highly. Moreover, it could increase the size of the bids by signaling to buyers that the object is valuable. Having the opportunity to try again to sell the good if there is no minimum bid is obviously an advantage; however, it can be a disadvantage if failure to sell the good the first time is seen as a signal of low quality to bidders in future auctions.

Why use an open auction? Recall that in order to avoid the winner ’s curse, each bidder in a common value auction will bid below his individual valua- tion. The greater the uncertainty about the true value of the object, the greater the likelihood of an overbid, and therefore the greater the incentive for the bidder to reduce his bid. (If the bidder is risk-averse, this effect will be magni- fied.) However, the bidder faces less uncertainty in an English auction than in a sealed-bid auction because he can observe the prices at which other bidders drop out of the competition—an advantage that provides information about their valuations. In short, when you provide more information to bidders, risk- averse bidders will be encouraged to bid more because they will be more confi- dent that they can account for the possibility of a winner ’s curse.

6. Bidding and Collusion

We have seen that sellers at auctions can obtain a significant share of the gains from trade by encouraging competition among buyers. It follows, therefore, that buyers can increase their bargaining power by reducing the number of bidders or the frequency of bidding. In some cases this can be accomplished legally through the formation of buying groups, but it may also be accom- plished illegally through collusive agreements that violate the antitrust laws. Collusion among buyers is not easy, because even if an “agreement” is reached, individual buyers will have an incentive to cheat by increasing their bids at the last minute in order to obtain the desired item. However, repeated auctions allow for participants to penalize those that break from the agree- ment by outbidding the “cheater” again and again. Buyer collusion is more of a problem in open-bid auctions than in the case of sealed bids because open auctions offer the best opportunity for colluding bidders to detect and punish cheating.

A well-known case of buyer collusion was the agreement in the mid-1980s among baseball owners to limit their bidding for free-agent players. The fact that such bidding was repeated and open made it possible for owners to retal- iate against those that bid too often and too aggressively. Collusion, however, is not limited to buyers. In 2001, two of the world’s most successful auction houses, Sotheby’s and Christie’s, were found guilty of agreeing to fix the price of commissions offered to sellers of auctioned items. Former Sotheby’s chairman Alfred Taubman was sentenced to a year in jail for his involvement in the scheme.

Source: Pindyck Robert, Rubinfeld Daniel (2012), Microeconomics, Pearson, 8th edition.

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