Today we commemorate a historic moment in auction theory. Twenty years ago, on July 25, 1994, the United States FCC began the first round of a new kind of auction based on suggestions of Paul Milgrom, Robert Wilson, and Paul McAfee. The spectrum auctions raised more than $10 billion and has been called the greatest auction in history. The auction marked the “era of putting auction theory to work,” and soon auctions with similar designs were held around the world.

In some ways, a successful auction is like a well-written book, an inspiring movie, or a beautiful theorem: everything just seems to work, and it is hard to appreciate the effort that went into the design of the finished product. It is only by contrast to pulp fiction, bad movies, and failed math pursuits that one can get a sense of how difficult it is to create something that works.

Therefore, we will celebrate the most successful auction by contrast. In this post, we highlight some of the crazy moments in the history of auctions to show examples of what can go wrong. In some cases strategic bidders can find ways to collude or game the auction. In other cases it is the designer to blame, for creating obviously bad rules or simply being incompetent. Two Nobel Prize winning economists make the list, and even the FCC spectrum auction has run into kinks. Auctions are hard to design; here are 4 of the crazy moments.

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"All will be well if you use your mind for your decisions, and mind only your decisions." Since 2007, I have devoted my life to sharing the joy of game theory and mathematics. MindYourDecisions now has over 1,000 free articles with no ads thanks to community support! Help out and get early access to posts with a pledge on Patreon. .

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1. Collusion in Turbines

This example is explained in The Art of Strategy.

In the 1950s, electric utilities bought turbines by soliciting bids from companies and then choosing the lowest price. Governments often use this kind of method when procuring contracts, with the idea being that it is a way to find the lowest price.

The problem is that companies and contractors might coordinate and find a way to keep prices high. Such collusion is against anti-trust laws, but a clever scheme might go undetected.

The three major turbine producers, GE, Westinghouse, and Allied-Chalmers, famously found a way to coordinate. They agreed that for a given contract, two of the companies would put excessively high bids–guaranteeing they would lose–and the third would put in a lower but highly profitable bid.

The question was, how could they coordinate their bids without being detected? Ingeniously, they based their bids on the lunar calendar. They agreed GE should win the bid on days 1-17 of the lunar calendar, Westinghouse on days 18-25, and Allis-Chalmers on days 26-28. The number of days reflected the market size of the companies, and since the bids came in randomly, the scheme allowed the companies to share high profits equitably.

The Department of Justice did eventually uncover the price-fixing in 1961, and some executives served jail time. The lesson for auction theorists is that bidders can be quite clever in collusion and sustain it for many years.

2. New Zealand Television

In 1990, New Zealand auctioned off its spectrum. To the government’s credit, it hired an economic consulting firm, NERA, to design the best auction. NERA suggested the government use a second-price auction, in which the highest bidder would receive the item at the next highest price.

Second-price auctions are theoretically great. Each bidder simply needs to submit a bid equal to what they are willing to pay. The item then goes to the person with the highest value and is sold at the second highest bid. The idea here is the person who wants the item the most gets it by slightly out-bidding the next highest bid. This is very similar to how eBay and open outcry auctions operate. So the choice of a second-price auction sounded like a good one.

However, there were two major problems for using it in New Zealand’s case. First, there were multiple identical items being sold. When seven licenses were sold, for instance, the auction could have been run as one big auction: the top seven bidders would get the license for the eighth highest price. However, New Zealand ran each auction independently. So in one case a firm that bid NZ$401,000 paid only NZ$100,000 for a license whereas another firm that bid NZ$255,000 won an identical license and paid NZ$200,000 for it. It makes no sense to charge less to a company willing to pay more, and it also makes no sense to charge different prices for identical items!

The second problem was much worse and embarrassing. In some of the auctions, the highest bid was much larger than the second-highest bid. In an extreme case, a company that bid NZ$7 million paid the second highest bid of NZ$5,000. The auction allowed the public to see companies were willing to pay much more for the auctions than they actually had to. Newspapers ran headlines about how horribly the auction went. The auction was expected to raise NZ$250 million; the actual revenue was only NZ$36 million.

The government should have set reserve prices and also made sure identical items sold for the same price. For example, they could have used a uniform price auction which is how US Treasury bills are sold.

3. A Nobel Fiasco

Ken Binmore helped design the 3G telecommunications auction for the British government, which raised $35 billion in 2000. In his book Playing for Real: A Text on Game Theory, he explains how misleading terminology resulted in two Nobel Prize winning economists getting auction theory wrong!

A little bit of background is necessary. Before 1991, the United States Treasury auctioned off its bonds in a pay-your-bid auction (also known as a discriminatory auction). In such an auction, the strategy is kind of like negotiating for a car: it not the smartest idea to reveal your true willingness to pay. You are better off being coy and pretending you would pay less.

Imagine the auction were instead run as a second-price auction for a single item–in which you paid the second highest price. Now there is no reason to conceal your willingness to pay. You will simply submit the most you are willing to pay, and then you get the item at the second highest price.

Now comes the kicker. The Treasury bond auction would not be run as a simple second price auction. As explained in the New Zealand example above, when you sell many identical items, you want to sell them at the same price. So the auction would be run where the highest bidders get the item at the next highest rejected price. Because all the items sell for the same price this is known as a uniform auction.

Now comes the kicker. Binmore explains, “In the finance literature, a uniform auction is called a second-price auction. The misleading terminology commemorates a memorable fiasco in which Nobel Prize winners Milton Friedman and Merton Miller…thought that a uniform auction would correspond to a second-price, sealed-bid, single-unit auction.”

Friedman said about the strategy in a uniform auction: “You need only know the maximum amount you are willing to pay for different quantities.” Merton similarly said, “You just bid what you think it’s worth. You wouldn’t need all this discussion beforehand about other people’s bids.”

The US Treasury did switch how it sold some of its bonds on this advice. The problem is that Friedman and Merton were wrong: in a uniform auction, there is always an incentive to shade one’s bid, known as the “inefficiently theorem.”

In this embarrassing moment at least the auction itself ran fine without a loss of tax money to the public. But it illustrates the danger of bad terminology.

4. The FCC Spectrum Auction

The 1994 FCC spectrum auction was wildly successful. Between 1994 and 1997, the auction raised winning bids worth $23 billion. But even the most successful auction method was not a perfect one. The auction had primarily been tested in laboratory experiments, and game theorists suspected that over time bidders might learn to outsmart the system.

In April 1997, one of the auctions signaled something was wrong, as reported in The Economist. An auction expected to raise $1.8 billion only raised less than 1 percent of that amount, at $13.6 million. The FCC suspected the bids were rigged and the Department of Justice went to investigate.

The bidders (legally) manipulated the auction by exploiting the bidding rules to signal aggressive bidding. In one case, a big bidder submitted two bids in the same round. Not wanting to get into a bidding war, competitors stayed out of the market and the price remained low.

In other case, Mercury PCS warded off a competitor High Plains Wireless through clever use of bidding. Mercury PCS modified its bid to include an area code for the region it wanted the license (for example $1 million might be submitted as $1,000,415 for a license in San Francisco). High Plains Wireless challenged this was signaling and collusive, but a court ruled that the bidding was in fact within the rules and allowed the FCC to grant the licenses won.

Game theorists had in fact warned the FCC this might happen in 1994 and offered a solution. The FCC did not make the change perhaps because attempts to warn off competitors can often backfire, leading to a bidding war. After the 1997 incident the FCC decided to adopt the simple solution: round all bids to an appropriate value to avoid the possibility of communication.

In Conclusion

These examples illustrate several principles. First, bidders are smart, they can be smarter than even the best auction theorists who try to design auctions that cannot be gamed. There are so many strategies to collude or communicate that eventually some bidders may find loopholes. When that happens, revenue dries up and the auction simply doesn’t work.

Second, even Nobel Prize winning economists sometimes get auction theory wrong, as the literature is vast and the math is complex.

So in short, auction theory is just hard. Let’s credit when the auctions work. Here’s to the past 20 years of putting auction theory to work and here is to developments for the next 20 years.

Sources and Further Reading

“greatest auction in history”

http://www.nytimes.com/1995/03/16/opinion/essay-the-greatest-auction-ever.html

“era of putting auction theory to work”

Paul Milgrom in his book Putting Auction Theory to Work

Collusion in turbines

The Art of Strategy, Chapter 3, page 92

New Zealand Television Source 1

Putting Auction Theory to Work, page 11-12

New Zealand Television Source 2

http://www.market-design.com/files/mcmillan-selling-spectrum-rights.pdf

Running the wrong auction source 1

Playing for Real: A Text on Game Theory, pages 618, 620

Running the wrong auction source 2 (Friedman WSJ)

http://cramton.umd.edu/econ415/auction-design-and-strategy.pdf

Running the wrong auction source 3 (Merton NYT and inefficiency theorem)

http://www.nytimes.com/1991/09/15/business/wall-street-diana-b-henriques-treasury-s-troubled-auctions.html

Even the FCC auction had its problems

http://www.economist.com/node/149797