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Monday, October 12, 2020

A Nobel Prize for Auction Theory: Paul Milgrom and Robert Wilson

Auctions are widely used throughout the economy. The big auction houses like Christie's and Sotheby's are well-known for selling famous art, and many people have either attended a live auction at a fund-raising event or a flea market or participated in an online auction at a site like eBay. But the behind-the-scenes uses of auctions are far more important. The right for online advertising to appear on your screen is sold in an auction format. When the US government borrows money by selling Treasury debt, it does so in an auction format. When electricity providers sign contracts to purchase electricity from electricity producers, they often use an auction format to do so. Some of the proposals for a buying and selling permits to emit carbon, as a mechanism for the gradual reduction of carbon emissions, would auction off the right to emit carbon. 

One useful property of auctions is that in a number of settings they can discipline the public sector to make decisions based on economic values, rather than favoritism. For example, when a city wants to sign a contract with a company that will pick up the garbage from households, companies can submit bids--rather than having a city council choose the company run by someone's favorite uncle. When the US government wants to give companies the right to drill in certain areas for offshore oil, or wishes to allocate radio spectrum for use by phone companies, it can auction off the rights rather than handing them out to whatever company has the best behind-the-scenes lobbyists.  In many countries, auctions are used to privatize selling off a formerly government-owned company.

But the bad thing about auctions is that (like all market mechanisms), they can go sideways and produce undesirable results in certain settings. The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2020--commonly known as the Nobel Prize in economics, was awarded to Paul R. Milgrom and Robert B. Wilson “for improvements to auction theory and inventions of new auction formats.” For some years now, the Nobel committee has also published a couple of useful reports with each award, one aimed a a popular audience and one with more econo-speak, jargon, and technical detail. I'll quote here from both reports: "Popular science background: The quest for the perfect auction" and "Scientific Background: Improvements to auction theory and inventions of new auction formats."

A useful starting point is to recognize that auctions can have a wide array of formats. Most people are used to the idea of an auction where an auctioneer presides over a room of people who call out bids, until no one is willing to call out a higher bid. But auctions don't need to work in that way. 

An "English auction" is one where the bids are ascending, until a highest bid is reached. A "Dutch auction"--which is commonly used to sell about 20 million fresh flowers per day--starts with a high bid and then declines, so that the first person to speak up wins. In an open-outcry auction, the bid are heard by everyone, but in a sealed-bid auction, the bids are private. Some auctions have only one round of bidding; others may eliminate some bidders after one round but proceed through multiple rounds. In "first-price" auctions, the winner pays what they bid; in "second-price" auctions, the winner instead pays whatever was bi by the runner up. 

In some auctions the value of what is being bid on is mostly a "private value" to the bidders (the Nobel committee suggests thinking about bidding on dinner with a Nobel economist as an example, but you may prefer to substitute a celebrity of your choice), but in other cases, like bidding on an offshore oil lease, the value of the object is at least to some extent a "common value," because any oil that is found will be sold at the global market price. In some auctions, the bidders may have detailed private information about what is being sold (say, in the case where a house is being sold but you are allowed to do your own inspection before bidding), while in other auctions the information about the object being auctioned may be mostly public. 

In short, there is no single perfect auction. Instead, thinking about how auctions work means considering for any specific context how auction rules and format in that situation, given what determines the value of the auctioned objects and what what kind of information and uncertainty bidders might have. 

If the auction rules aren't set up appropriately, the results can go sideways. For some example, Paul Klemperer wrote a some years back on the subject of "What Really Matters in Auction Design." 
One of his examples was about what happened in 1991, when the UK used a process of sealed-bid auctions to see what company would be allowed to provide television services in certain areas. Klemperer writes: 
The 1991 U.K. sale of television franchises by a sealed-bid auction is a dramatic example While the regions in the South and Southeast, Southwest, East, Wales and West, Northeast and Yorkshire all sold in the range of 9.36 to 15.88 pounds per head of population, the only—and therefore winning—bid for the Midlands region was made by the incumbent firm and was just one-twentieth of one penny (!) per head of population. Much the same happened in Scotland, where the only bidder for the Central region generously bid one-seventh of one penny per capita. What had happened was that bidders were required to provide very detailed region-specific programming plans. In each of these two regions, the only bidder figured out that no one else had developed such a plan.
Another problem arises if the bidders find a way to signal each other to hold prices down. In some cases, the bidders can use the bidding process itself to send messages. Here's an example from Klemperer: 
In a multilicense U.S. spectrum auction in 1996–1997, U.S. West was competing vigorously with McLeod for lot number 378: a license in Rochester, Minnesota. Although most bids in the auction had been in exact thousands of dollars, U.S. West bid $313,378 and $62,378 for two licenses in Iowa in which it had earlier shown no interest, overbidding McLeod, who had seemed to be the uncontested high bidder for these licenses. McLeod got the point that it was being punished for competing in Rochester and dropped out of that market. Since McLeod made subsequent higher bids on the Iowa licenses, the “punishment” bids cost U.S. West nothing (Cramton and Schwartz, 1999).
Notice that the bids from U.S. West ended in the number 378, which was the lot number where the company wanted McLeod to back off. 

Of course, concerns like these have obvious answers. For example, set a "reserve price" or a minimum price that needs to be bid for the object, so no one gets it for (nearly) free. Also, set a rule that all bids need to be in certain fixed amounts, and that increases in bids also need to be in fixed amounts. But making these points both raises practical questions of how this should be done, and also shows some ways in which the practical rules of auctions can matter a lot. 

A more subtle but well-known problem with auctions is called the "winner's curse." It was first documented in the context of bidding by companies for off-shore oil leases. An analysis of the bids, along with how much oil was later discovered in the area, found that the "winner" of these auctions was on average losing money. The reason is that each individual company was forming its own guess about how much oil was on the site. Naturally, some companies would be more optimistic than others, and the most over-optimistic company of all was likely to bid highest and "win" the auction. A problem is that once bidders in an auction become aware of the risk of the winner's curse, they may become very reluctant to bid, so that the bids stop representing the actual estimates of value. 

In professional sports, this kind of scenario often plays out when free agents try to encourage bidding among teams for their services. From the player point of view, it only takes one high-end bidder, a bidder who perhaps is ignoring the winner's curse, to get a great contract. But many teams may decide to avoid the risk of overpaying and the winner's curse by not bidding at all. 

There are various possible responses to a winner's curse in an auction format. One is to find ways for the bidders to collect more private information, so that they can be more confident in their bidding. Another is a "second-price" auction, where the winner pays the price of the second-highest bidder. This format provides some protection against the winner's curse: that is, everyone can feel free to bid as high as they would like, knowing that if they are way out of line with the second-price bid, they will only have to pay the second-price bid. If a second-price bid greatly reduces concerns about the winner's curse and leads to more aggressive bidding, it can (counterintuitively) end up raising more money than a first-price auction. 

The auctions that most people participate in are "private-value auctions," where the issue is just how much do you want it--because you are planning to use it rather than to resell it. In this setting, a live auctioneer tries to get people emotionally involved in how much they want something, and in this sense to get them to pay more than they had perhaps planned to pay beforehand. As Ambrose Bierce wrote in his Devil's Dictionary published back in 1906: "AUCTIONEER, n. The man who proclaims with a hammer that he has picked a pocket with his tongue."

But auctions for oil leases, spectrum rights, privatized companies, Treasury debt, an so on have some element of being "common value" auctions, where the value of what is being sold will be similar across  potential buyers. As the Nobel committee writes: "Robert Wilson was the first to create a framework for the analysis of auctions with common values, and to describe how bidders behave in such circumstances. In three classic papers from the 1960s and 1970s, he described the optimal bidding strategy for a first-price auction when the true value is uncertain. Participants will bid lower than their best estimate of the value, to avoid making a bad deal and thus be afflicted by the winner’s curse. His analysis also shows that with greater uncertainty, bidders will be more cautious and the final price will be lower. Finally, Wilson shows that the  problems caused by the winner’s curse are even greater when some bidders have better information than others. Those who are at an information disadvantage will then bid even lower or completely abstain from participating in the auction."

But when you think about it, many of these "common value" auctions actually have a mixture of private values as well. For example, consider bidding on an offshore oil lease. The value of any oil discovered may be a common value. But each individual company may have specific technology for discovering or extracting oil that works better in some situations that others. Some companies may also already be operating nearby, or have facilities nearby. In short, lots of real-world auctions are a mixture of private and common values. As the Nobel committee writes: 
In most auctions, the bidders have both private and common values. Suppose you are thinking about bidding in an auction for an apartment or a house; your willingness to pay then depends on your private value (how much you appreciate its condition, floor plan and location) and your estimate of the common value (how much you might be able to sell it for in the future). An energy company that bids on the right to extract natural gas is concerned with both the size of the gas reservoir (a common value) and the cost of extracting the gas (a private value, as the cost depends on the technology available to the company). A bank that bids for government bonds considers the future market interest rate (a common value) and the number of their customers who want to buy bonds (a private value). ... The person who finally cracked this nut was Paul Milgrom, in a handful of papers published around 1980. ... This particular result reflects a general principle: an auction format provides higher revenue the stronger the link between the bids and the bidders’ private information. Therefore, the seller has an interest in providing participants with as much information as possible about the object’s value before the bidding starts. For example, the seller of a house can expect a higher final price if the bidders have access to an (independent) expert valuation before bidding starts.
In addition, Milgrom has participated in setting up new kinds of auctions. When auctioning radio spectrum to telecommunications providers, for example, how much you are willing to bid for rights in one geographic area may be linked whether you own the rights in an adjoining area. Thus, rather than auctioning off each geographic area separately--which can lead problems of collusion between bidders-- it makes sense to design a Simultaneous Multiple Round Auction, which starts with low prices and allows repeated bids across many areas, so that geographic patterns of ownership can evolve in a single process. There is also a Combinatorial Clock Auction, in which bidders might choose to bid on overall “packages” of frequencies, rather than bidding separately on each license. Milgrom also was a leading developer of the Incentive Auction, which the Nobel committee describes in this way;
The resulting new Incentive auction was adopted by the FCC in 2017. This design combines two separate but interdependent auctions. The first is a reverse auction that determines a price at which the remaining over-the-air broadcasters voluntarily relinquish their existing spectrum-usage rights. The second is a forward auction of the freed-up spectrum. In 2017, the reverse auction removed 14 channels from broadcast use, at a cost of $10.1 billion. The forward auction sold 70 MHz of wireless internet licenses for $19.8 billion, and created 14 MHz of surplus spectrum. The two stages of the incentive auction thus generated just below $10 billion to U.S. taxpayers, freed up considerable spectrum for future use, and presumably raised the expected surpluses of sellers as well as buyers.
The economic theory of auctions is clearly tied up in intimate ways with the practice and design of real-world auctions. More broadly, close analysis of buyers and sellers in the structured environment of auctions can also offer broader insights into how non-auction markets work as well. After all, in some ways a competitive market is just an informal auction with sellers offering bids hoping to get a higher price and buyers making offers hoping to get a lower price. 

For more from Milgrom and Wilson on auctions and related economics, here are some articles from the Journal of Economic Perspectives, where I work as Managing Editor. 
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