The Nobel Prize in Economics 2020 was awarded to Robert Wilson and Paul Milgrum for developing the theory of auctions and inventing their new formats. This is by no means the first prize on the subject: William Vickery in 1996, Leo Gurwich, Roger Myerson and Eric Maskin in 2007 received the Nobel Prize for Theoretical Mechanisms and Alvin Roth for Practical Market Design. What is so special about auctions and their creation? Explains NES Professor Sergey Izmalkov.
Auctions all over the place
Auctions are used everywhere, usually invisible to citizens. Every time a user watches a video, reads a blog or simply looks for information, an auction is held among advertisers for the right to show ads to this particular user. Google, for example, conducts trillions of such auctions a year, and this is the main source of income for the company. The lion’s share of goods and services purchased for the needs of the state or large private companies is carried out through auctions or similar competitive procedures. Privatization of enterprises and other assets, sale of licenses or quotas for any activity, frequencies for mobile communication, development of deposits, fishing, deforestation – all this is done through auctions. Double auctions, static and dynamic, are exchange trading mechanisms, financial instruments, energy and other resources. You can buy almost everything on the auction online platform eBow. And if you suddenly want to sell a car or an apartment, the ideal situation is to find several potential buyers and choose the one who will offer the highest price – and this is nothing but an auction.
An auction is a procedure, as a result of which it is quickly determined, who bought (or sold) and at what price. For the sale of one item in the first price auction, bidders bid and the highest bidder gets the item, and the price becomes the item. In a dynamic up-price auction or English auction, bidders shout out at each other, making higher and higher bids. The one who placed the last bid wins (gets the item). The price is his own bid if jumping is allowed, or the last bid of a competitor if the auction is held without jumping.
Often, in an auction such as the sale of art objects, the auctioneer gradually raises the bids himself and does so until there is only one active bidder left. Exactly the same auction was used in ancient times to sell slaves, property of debtors, and even once the entire Roman Empire, when in 193 AD the emperor was Didius Julian, who promised the Praetorians more money than a competitor in the open auction. He, however, only lasted a couple of months and was killed by the same Praetorians. The curse of the winner?
Values of participants
The success of auctions is explained simply. If you ask a question about how to sell an item optimally (so as to get the maximum income) or efficiently (so that as a result the item gets the one who values it most), the answer in both cases in different situations will be an auction. Auctions are especially good in situations where there is no market, when the goods are few and how many bidders are willing to pay is known only to them.
Roger Myerson brought out the optimal auction, and William Vickery suggested an effective mechanism to redistribute many goods. The fact that the English auction has been used unchanged for thousands of years has a simple evolutionary explanation – there is no better mechanism. An English auction is effective and optimal if you add a correctly chosen reserve price and if there is no additional information about the bidders.
All this is true if the participants’ values are private. And Robert Wilson and Paul Milgrom built the theory of auctions with common and interdependent values. What does this mean?
A participant’s value is the maximum amount that they are willing to pay for an item. Maybe the bidder doesn’t know for sure the value he can get from the item, and then the value expresses the expected value of the item, expressed in money. The value is private if the expected usefulness of the goods does not depend on how the goods are valued by the other members. In an English auction for private value situations, it is beneficial for a bidder whose value is, say, 1000 to continue to bid until the current price is less than 1000 and to stop participating if the price exceeds 1000. When all participants act optimally, the one whose value is the highest will win.
But for many products, values are not private. For example, when selling the rights to develop a gas field, different participants may have different estimates of the amount of gas and the complexity of its production and transportation, and therefore the expected profit, but the gas is the same regardless of who wins. If participants shared their information, they would recalculate the expected profit and would likely have approximately the same values. This is a case of shared values.
The curse of the winner
Robert Wilson drew attention to the auctions with common values and to the effect of “curse of the winner”. Let’s assume that the rights to develop the deposit are distributed through the first price auction. Then the bidder with the highest bid is likely to be the one whose individual profit evaluation was the most optimistic. Once he wins the auction, he gets an information blow: he learns that everyone else’s grades are lower than his. This allows him to recalculate the expected profit and lower his score. And this means that if a rational participant wants to avoid the curse, he should take this effect into account – instead of his personal evaluation from the very beginning, he should use the conditional profit recalculated as if he had won in anticipation of more pessimistic evaluations of his competitors.
Paul Milgrom later considered a more general case of values – interdependent values, where the value of participants may depend on information held by other participants, including the seller, but is not required to be the same for all. In the gas field example, participants may own neighboring sites or run their own tests to determine a field’s capacity and trust their estimates more than their competitors. As a result, even if they knew the competitors’ information, the expected values would be different. Paul compared several auction formats in terms of expected profit and efficiency and got a fairly general result that disclosure in the bidding process increases both the seller’s profit and efficiency.
In English auctions, by observing the activity of competitors, participants can overestimate their expected profit during the auction. At any current price, they should do it as if their competitors’ bids were the last, i.e. they should think pessimistically about their competitors. In this case, if the competitors really stop bidding, the bidder will not have an information blow and will be able to avoid the curse of the winner. If the competitors keep betting, it is possible to increase the expected value.
It is this conclusion – about the possibility in open auctions with higher prices to disclose the necessary information from competitors and thus reduce uncertainty in the estimates of expected profits – that formed the basis of numerous practical designs, which Robert and Paul and his colleagues have proposed and continue to propose and improve for the sale of various products.
In particular, for the first U.S. communications frequency allocation auction in 1994, they offered a multiround open auction. In such an auction, several different products (broadcasting licenses for a certain band in the case of frequencies) are sold simultaneously: bidders in each round can increase their rates with a certain step from the current prices. At the end of the round, intermediate winners and prices for them are counted at the current rates, which allows to overestimate their values and take into account information contained in the competitors’ rates. Current winners do not need to raise their bids conditionally on their goods: the auction will end when there are no new bids. This format allows participants to bid on the most attractive goods for them, taking into account current prices, and jump from some goods when they become too expensive to others.
Such a relatively complex auction compared to the format “wins those who made higher bids in a one-round auction” was successful, dispelled doubts about the benefits of careful choice of format and gave impetus to further development of theory and practice. The effect of careful choice of auction format can be huge, as shown by the famous example with auctions on frequency distribution for 3G mobile communications in Europe in 2000-2001. The UK auction brought 2.5% of GNP or €650 per capita to the budget. And in Switzerland – only €20. The ability of Swiss citizens to pay, their demand for mobile communications, and thus, the expected profit was hardly less than in the UK. The problem turned out to be in the choice of format, or more precisely, in the inattention to competition. There were exactly four applicants for four licenses in Switzerland after the participants were allowed to join consortia.
Robert Wilson and Paul Milgrom are not only famous for their achievements in auctions. They have many fundamental works in other areas as well. It is amazing that Wilson raised a whole galaxy of famous economists, three of whom – Alvin Roth, Bengt Holstrom and Paul Milgrom – received the Nobel Prize.
The achievements of this year’s laureates show how theory and practice are interconnected: practical issues pose challenges to theory, the results of which, in turn, provide an opportunity to change practice. Surprisingly, the awardees participated in this process from all sides – both in setting the task, in analyzing models, in designing new formats, and in their implementation.