Chapter 18
Knowing How to Win at Auctions
In This Chapter
Distinguishing the different types
Seeing how bidders behave at auctions
Dealing with the problem of the winner’s curse
People often associate auctions with the sale of antiques and artworks, often sold in specialist auctions run by famous auction houses such as Christie’s or Sotheby’s. For example, in June 2006 Christie’s in New York auctioned Vincent van Gogh’s painting Portrait of Dr. Gachet for $82 million (which, allowing for inflation over the last ten years, amounts to $152 million in today’s prices — not bad for a man who sold only one painting during his lifetime). Or they think of auction sites on the Internet, like eBay, where you can bid on just about anything imaginable.
But all sorts of other things can be auctioned, too, and they don’t need to be physical objects. The U.S. Federal Communications Commission auctions off valuable parts of the radio spectrum to mobile phone networks. Since 1994, it has conducted more than 85 auctions and raised roughly $60 billion for the U.S. Treasury.
In an auction, the seller tries to maximize the value of the assets that it wants to sell. More potential buyers exist than assets, so the seller attempts to use the mechanism design of an auction to reveal the value that buyers ascribe to the asset in order to get the highest price possible.
Auctions can be devilishly tricky things to participate in, with sellers and bidders using all sorts of tactics and maneuvers. In this chapter, we talk you through some of the features of auctions and introduce you to the underlying theory behind auctions from the seller’s, the bidder’s, and the auctioneer’s perspective. We show you why auctions are such a useful tool for allocating assets, and that despite their positive features, they also have some limitations and downsides — even for the auction winner.
Spotting Different Kinds of Auction
The term auction is a category rather than a specific thing. Many different types of auction exist, each with advantages and disadvantages depending on whether you take a seller’s, a buyer’s, or even society’s perspective. They all have a mechanism in which an auctioneer solicits bids for the item under the hammer, but they vary in the means they take to get to the final sale price.
Economists have explored many existing types of auction using economic theory and discovered that the results vary from auction to auction. They’ve found that being specific about the design pays off when describing individual types of auction.
An auction can be considered a refinement of the conditions of a monopoly, with only one seller and several buyers. When only one buyer exists, the condition is a bilateral monopoly, and the good is more likely to be disbursed by negotiation than auction. The price that buyers pay is likely to be above the marginal cost of the item, and so auctions do mean that surplus tends to go to the seller.
Knowing the type of auction you’re in
Here are the most common attributes of the many types of auction. Often these types aren’t mutually exclusive, so you can talk about a sealed bid, second price, English auction (flip to the later section “Making bidders honest with a Vickrey auction” for more on this type of auction):
- English auction: The most familiar type, from auction scenes in films and on TV. The auctioneer starts at a floor price — a minimum price below which the good won’t be sold, usually selected by the auctioneer who represents the seller — and successive bids raise the price until the item is eventually sold to the highest bidder.
- Dutch auction: The price starts at a price ceiling and each successive round consists of the auctioneer dropping the price until someone takes the item.
- Open outcry: Each bidder reveals his bid to all other bidders by calling out the sum he wants to pay to receive the lot.
- Sealed bid: Bidders submit their bids in sealed envelopes, so that other bidders don’t know the bids. Variants can include different degrees of disclosure required of bidders or the auctioneer.
- First price: The winning bid is the highest declared bid when the auctioneer finally says, “Sold!”
- Second price: The winning bidder pays the second-highest declared bid. So, if you’d bid $100 and the winner had bid $110, the winner finally pays $100 (your second-highest bid) when he comes to take the goods home. This refinement gives bidders the incentives to bid how much the item is worth to them, and not to misrepresent their valuation of the good.
- Reservation (or reserve) price: A variant with a floor price, below which the item isn’t sold (check out the later section “Setting a reservation price wisely” for more details).
- Online auctions: Sometimes these allow the seller to set a price at which the auction ends and the item goes to the first bidder to meet the “buy it now” price.
The other major distinction that economists make between auctions concerns what’s being sold:
- Private-value auctions: Every bidder may have a different valuation for the good in question, as is the case for art auctions.
-
Common-value auctions: The good has the same value for every participant, but because of uncertainty their estimations of that value may differ. This case applies for some mineral-rights auctions, where the rights have the same value, and bidders differ by belief.
Suppose, for example, that 10 billion barrels of oil are under Dallas Airport, and the rights to drill are being allocated in an auction. Every potential bidder would get the same amount of oil if they win the auction. However, the amount that they’re willing to pay depends on their belief about how much that oil would be worth to them; the amount may vary wildly among the bidders if they have different costs of extracting the oil or different beliefs about how much they’d make from selling it.
Designing an auction to get (most of) what you want
Economists are often asked to give their opinions on which particular kind of auction is best for a particular situation. They usually express their answer in terms of two criteria:
-
Pareto efficiency (or optimality): The outcome of the auction should be Pareto efficient, meaning that making one party better off without making another party worse off isn’t possible.
- Profit maximization: The auction should yield the highest expected profit to the seller.
Given these criteria, as the economist you can examine some of the auction types and score reasons to prefer one or another in a particular context.
An auction is a type of mechanism design and is similar to designing a game that players play. When you design a mechanism, you’re assuming that players have privileged information over their own strategies but that the expected payoffs are known to the designer. We discuss mechanism design more fully in Chapter 16.
Meeting an auction’s two core criteria
For the mechanism to be Pareto efficient, the good must go to the bidder with the highest bid. To see why, suppose two bidders bid for a good. Bridgette bids $100 and Brian bids $80, but suppose for some reason Brian gets the good. If he then sells the good to Bridgette for $90 both parties make themselves better off without making anyone worse off. So the result of the auction couldn’t have been Pareto efficient. (The seller, by the way, is part of the original auction, not the subsequent transaction, and here the focus is on whether the allocation between the bidders is Pareto efficient.)
When you know every bidder’s valuation exactly, profit maximization for the seller is easy. The question is what to do when the auctioneer or seller doesn’t know their valuations. Here, examining the different types of auctions with economic theory helps. But the answer can only “help” rather than “exactly predict,” for the simple reason that the behavior of the bidders depends on their true beliefs about the value of the good, which the auctioneer doesn’t know.
Setting a reservation price wisely
One way to increase the likelihood of maximizing profits in an auction is to set a reservation price — a minimum price lower than which the good won’t be sold. Sometimes the reservation isn’t met, but in all other cases, the auctioneer is certain of getting a level of profit above the reservation.
On the online auction site eBay, there are over 81 million active users and billions of goods are auctioned off annually. Minimum reserve price or minimum starting bids are common in eBay auctions, and evidence from eBay suggests that higher reserve prices decrease the number of bidders and increase the likelihood that the good is sold. Conditional on a sale occurring, setting a higher minimum reserve price does increase the expected revenue of that sale.
When you set a reservation price, sometimes you’ll fail to sell the item, meaning that Pareto efficiency is not achieved. Having a reservation price still maximizes expected profit even though sometimes the auction fails. In this case, you’re trading off between Pareto optimality and profit maximization.
Bidding for Beginners
The most important piece of advice that economists have for bidders in an auction is: Read the rules carefully. Optimal bidding strategy varies wildly among the different auctions, and because some types (check out the earlier section “Knowing the type of auction you’re in”) can be significantly more complex — especially in awarding huge procurement contracts — make sure that you have all the small print covered.
Modeling a simple auction
Despite the warning that opens this section, some of the simpler types of auction are easy to model.
Lawrence Friedman’s analysis of a lowest-price, sealed-bid, common-value auction provides one such framework. Suppose there are a number of painters, say N, bidding on a contract to paint a historic home. Each painter bids an amount of what they want for doing the job — say bi — where i is the number of the bidder. The lowest bid wins the job. If a bid b wins, the yield is b – c, where c is the cost incurred by each of the painters to do the job.
The probability that painter i’s bid bi is lower than the bid b is equal to
F indicates the likelihood of any individual bidder bidding less than the bid, b.
If the winning bid is b, that means that the other bidders N – 1 have submitted a bid that has a winning probability of 1 – Fi(b). Because probabilities must sum to 1, the probability of something not happening for a bidder is 1 – F.
The probability of winning the bid is equal to the probability of the other N – 1 bidders not winning, so we can expand the expression for winning in terms of all other participants losing. For N – 1 other bidders, it must equal
Expected profit of the winning bidder is
where P(b) indicates the probability of winning the bid. This is the expression that Friedman recommends maximizing.
To do that, you want to have as much information as possible about other bidders’ past bidding behavior.
One challenge for contractors bidding on a job in a sealed-bid auction is knowing what their costs of doing the job will be. Contractors have a best guess at what a contract will cost without really knowing what’s going to happen to costs over that period. For instance, when bidding for the contract to repair the Enterprise Canal Bridge in Idaho, a company may have a plan and some guesses on how much the contract will cost, but the firm can’t know exactly and thus may still get caught out bidding too low because costs turn out to be higher.
Providing advice on a bidding strategy means you may have to make assumptions about the costs and/or benefits of the future value of the item.
For instance, if you know that Mondrian’s reputation in the art world is about to take a tumble — hey, art is a rough world! — then the rational decision is to bid a lower price in an upcoming auction, because the value of the option to resell the item is going to be lower. Of course, as a Mondrian fan, the art value received from the item may be enough for you to contemplate bidding sub-optimally high for the item. If the auction is a private-value auction, this is all that matters to you — whether you personally value the item at the bid price. For a common-value case, on the other hand, the expectation of what will happen to the value of the item is important.
Bidding late: The Internet auction phenomenon
An open-outcry, English auction allows successive rounds of bidding to reveal more information about the valuations of successive bidders, which isn’t the case in — for instance — a Dutch auction (see the definitions given earlier). It definitely is the case, though, in an Internet auction, which is generally structured as a Vickrey auction (more on these in the later section “Making bidders honest with a Vickrey auction”).
An Internet auction goes through successive rounds of bidding up to a final deadline. What’s interesting is that a high percentage of bids are made close to the deadline — around 37 per cent in the last minute. The Internet auction house eBay calls this strategy sniping.
Economists have come up with two explanations for sniping:
- Bidders don’t want to tip their hand to other bidders: If you’re an expert on, say, rare guitars, and the auction site is designed to display your profile with your bid, then you may want to delay bidding to prevent other people from knowing of your interest in, say, that rare Gretsch White Falcon.
- Implicit collusion between buyers: In the case of an auction, collusion means that the bidders have coordinated their strategies by waiting until the last few moments before the auction ends (of waiting until the last few moments before bidding), so there is less time for bidders to bid up the price.
Imagine a second-price auction, where the prize is a White Falcon guitar worth $6,000, with a reserve price of $2,000. If two bidders start their bids early and both honestly state their true value as $6,000, they’ll end up with one receiving the guitar for $6,000 — great for the seller, but the buyer gets no consumer surplus. Suppose instead that they wait until the last second. Now only one of those bids may get through, and by the second-price rule of the auction, that bidder ends up paying the reservation price of $2,000!
Gaming an auction
Auctions are useful for revealing the value that a buyer is willing to pay for an item. Sometimes, though, auctions fail to work out the way the auctioneer or the buyers want. Dodgy behavior can take place on both sides of the deal, with buyer and seller possibly having incentives to take the process away from a true and fair auction, just as they may do in a cartel (discussed in Chapter 16).
Although auction design can mitigate these “gaming” factors, you also need to be on the lookout for bent auctions, which occur when auction rules are broken or bent, like trying to learn what others are bidding in advance of making a bid. Authorities and regulators often are on the lookout and can get bent out of shape about it.
Trying to avoid an auction
In certain cases, forcing someone not to auction something can be a viable strategy.
When negotiating for the transfer of the talented Welsh soccer player Gareth Bale from Tottenham Hotspurs, the buying club Real Madrid — allegedly — tried everything to make sure another potential buyer wasn’t found. Why? Well, Tottenham could’ve leveraged the two potential buyers against each other to get a higher price for the player. Eventually Real Madrid paid an undisclosed sum believed to be around 90 million euro ($99 million) for Bale’s services. If another bidder had emerged, the final sum might well have been even higher.
Colluding
Sometimes bidders collude by not making competitive bids against each other or by pooling their bids and redistributing the returns after the auction.
Bidder collusion is illegal and is a potentially pervasive problem. Not surprisingly, it is a target for antitrust enforcement. In 1990, the U.S. General Accounting Office reported that from 1982 to 1988, more than half of the criminal restraint of trade cases filed by the U.S. Department of Justice’s Antitrust Division involved auction markets. If a cartel is operative, then it is easy to see how it could instruct its highest-valuing member to bid a value while all other cartel members bid some amount below the auctioneer’s reserve price.
Summoning buyers
An auctioneer can receive a higher price for a good by summoning a phantom buyer. Imagine an art auction where a phone bidder is in cahoots with the auctioneer and keeps phoning in a bid increment until the auctioneer guesses that he isn’t going to get away with raising the price any higher. More potential buyers are therefore kept in the game (even if one isn’t real), competing against each other to raise the price.
This situation — again, allegedly — was encountered in a soccer transfer where the selling club “found” a bidder very late in the process who was willing to pay double the eventual buying club’s initial bid. The buying club decided to bite the bullet and pay the fee. The selling club received double its expected compensation for the transfer.
In case you’re wondering, transfers of star team players can often appear murky because of the amount of private information involved and the relatively low requirements for disclosure compared to many other industries.
Suffering from the Winner’s Curse
Oscar Wilde famously identified two tragedies in life: not getting what you want and getting what you want. The winner’s curse is a problem that comes from winning an auction.
Essentially, the problem is that in an English, first-price auction, bidders always have an incentive to bid more than they can afford to get an item — and, of course, the auctioneer has no knowledge of what they can afford and is unable to know this until the auction concludes.
This issue is primarily a problem with common-value auctions — where the true value of the item isn’t known. In bidding for a sports franchise, airwave spectra, mineral rights, or broadcast licenses, it’s a perennial problem, because the true monetary value of those items is never known in advance. Microeconomics is often used to look at the allocation of goods and services, and so this makes the incentive to bid too high a real economic problem — whether you’re designing the auction or bidding in one.
Making bidders honest with a Vickrey auction
Auction houses can mitigate the bidding-more-than-you-can-afford problem in a number of ways. For instance, they can require a bank guarantee before someone enters the auction, so that if a person doesn’t have evidence of being able to afford the good, he can’t enter the race for the Gauguin.
But consider the problem of a government auction of a valuable license. In this case, the winner itself may not know that it has been cursed until sometime into the period of the license.
The International Olympic Committee (IOC) is an organization whose bidding contests attract a great deal of attention. Major cities see hosting the games as an opportunity to attract tourists and be the center of international attention. However, overbidding for hosting the winter or summer Olympic Games may not be revealed until well after the last gold medal has been won. The host city that overbids for the games may be left with a debt burden, often in the billions of dollars, that taxpayers will have to foot the bill for. The fear of overbidding was a motivating force in the 2015 No Boston Olympics, a volunteer-based group that was persistent and successful in spreading its message that hosting the 2024 Summer games in Boston would be risky and expensive and would leave taxpayers on the hook with no economic gains. The city’s quest to host the games soon came to an end when the U.S. Olympic Committee pulled the plug on its bid.
Meeting the Vickrey auction
One of the auction designs that doesn’t have an incentive to overbid is the sealed-bid, second-price, English auction, better known as a Vickrey auction after celebrated Canadian economist William Vickrey.
In a Vickrey auction, the item under the hammer goes to the bidder who submitted the highest bid, but at the price bid by the second-highest bidder. This design removes the incentive to bid too high, because the price that’s eventually accepted is the second bid.
In an English auction, the good goes to the highest bidder at the price that bidder was willing to pay. The result is therefore Pareto optimal (as explained in the earlier section “Designing an auction to get (most of) what you want”). In a Vickrey auction, participants make sealed bids, which gives them an incentive to bid a value that honestly reflects their valuation of the bid. But in a standard English sealed-bid auction, this isn’t necessarily the case. How does changing from a standard auction to a Vickrey auction change things?
Seeing the Vickrey auction in action
Suppose two bidders, bidder1 and bidder 2, have valuations for a good, v1 and v2 respectively, and bid b1 and b2 for it. The expected payoff for bidder 1 is
You don’t need to consider the case where b2 is bigger than b1, because in that case bidder 1 receives 0, and the expected payoff is zero.
Two possible bidding cases exist that get the best payoff:
- When v1 is bigger than b2: In this case, bidder 1 is best off when making the probability of a winning bid as high as possible. Thus, given that his valuation of the item is v1, he makes b1 as high as makes sense and so he sets b1 = v1, his true valuation of the item.
- When v1 < b2 and bidder 1 wants to make the possibility of winning as small as possible: How would bidder 1 best do that? Well, by bidding v1. That way, bidder 1 is unlikely to win the auction and would get the best possible value by bidding less than the valuation of the person who wants it most, which would be bidder 2.
The key point here is that in either case, the incentive for the bidder is to declare his true valuation of the bid. In both the cases, the most important factor is that if the auction is set up in this way, no one has any incentive to bid other than his true valuation of the good.
Perusing the curse in public procurement
When the government auctions to bidders a license to operate some activity, it’s trying to do the best for the public purse by maximizing the value it gets for the license under auction. The problem is that because the government and the bidder don’t know what the costs or the expected revenues of the winning bid will be, public procurement contracts are often subject to winner’s curse problems.
Typically, a public procurement auction tends to be a sealed-bid, lowest-price auction. Bidders bid for the lowest possible contract fee they can get from the government, the one with the lowest fee getting the franchise.
Even if the auction is completed at the second price, however, because winners don’t know exactly how the revenues and costs of the franchise will work out, situations still exist in which the franchise may prove to be too expensive to operate. Typically, these issues are mitigated through the contractual system, so that the franchise may be conditional, and the government or bidder can cancel the agreement (often subject to penalties).
Clearly, therefore, the ability of mechanism design to bring order to an uncertain world is limited. Often both designer and bidder are subject to significant uncertainties, and more importantly, they both have a rationale for measuring the uncertainties and a technique for mitigating the penalties of getting things wrong. A bid is always an estimate, in these cases, of the value of the contract rather than a direct valuation of the contract, so don’t be too hard on parties that make errors. Being wrong about uncertain futures is easy — people ever getting such things right is more surprising.