Milgrom and Wilson Awarded Nobel Prize in Economics

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It was announced on October 12^th at 11:45 CEST by the Royal Swedish Academy of Sciences that the 2020 Nobel Memorial Prize in Economic Sciences was awarded to Professors Paul Milgrom and Robert Wilson “for improvements to auction theory and inventions of new auction formats”. The two American academics teach at Stanford University and, with their award, all 2020 Nobel prizes have officially been announced.

The Academy’s press release states: “This year’s Laureates, Paul Milgrom and Robert Wilson, have studied how auctions work. They have also used their insights to design new auction formats for goods and services that are difficult to sell in a traditional way, such as radio frequencies. Their discoveries have benefitted sellers, buyers and taxpayers around the world.”

Who are Milgrom and Wilson?

Professor Wilson, who was woken up in the early morning (California time) by a call from the Prize Committee, earned his PhD in 1963 from Harvard Business School. His work spans several fields heavily reliant on game theory, including industrial organization and information economics, and his initial contributions where especially relevant for mathematical economics and optimization theory. In a video recently published by Bocconi University on social media, Professor Marco Ottaviani, whose advisor’s advisor was Robert Wilson, said that “Bob is a wonderful and generous mentor who really believes in the power of science and economics in making the world a better place by talking to practitioners”.

Professor Milgrom, who is reported by Reuters to have been woken up at 2:15am California time by his neighbor, Professor Wilson, knocking on his door with the exciting announcement, earned his PhD in 1979 from Stanford University. Wilson was his doctoral advisor. His focus has been on auction theory from very early on, starting with his PhD dissertation, but his work extends to game theory, mechanism design and mathematical methods for economics. The professor has also cofounded several companies, most notably Auctionomics, a world leading auction consulting company. The cofounder and CEO of Auctionomics is Bocconi graduate Dr. Silvia Console Battilana. The Economist magazine has reported that Professor Milgrom’s consultancy was instrumental in saving a company $1.2 billions in a spectrum auction.

What is auction theory?

The first thing that comes to mind when the word “auction” is mentioned is probably the art market. Big names such as Sotheby’s and Christie’s dominate the news in the business, and their auctions are often publicized well beyond the few rich financiers and investment bankers who can afford to participate in one. Most recently, Christie’s auction of Leonardo da Vinci’s Salvator Mundi, sold for $450.3 million on 15 November 2017, was thoroughly covered by the mainstream media and curiously followed by millions.

Auctions differ in two main respects: format and information. Those carried out by Sotheby’s or Christie’s are known as English auctions. In that format, the auctioneer starts the bidding at a low price and gradually increases it. The highest bidder gets the item. Dutch auctions, on the other hand, start from a high asking price which is then lowered until one participant accepts to pay it. This format takes its name from the way tulips and other flowers are sold in Holland.

Two other very relevant formats are first-price sealed bid auctions and second-price sealed bid auctions. In the first-price sealed format, bidders indicate secretly, simultaneously and independently the price they are willing to pay for the item. This format is the standard in government tendering. In second-price sealed auctions, the only difference is that the highest bidder gets the item but has to pay the price submitted by the second-highest bidder. This latter format is known to be used by eBay. As far as information is concerned, auctions differ mainly in two respects: what the bidders know about the value of the auction item and what they know about each other’s private valuation of the same.

Auction theory started as a research pursuit in the Sixties, when the 1996 Nobel laureate in Economic Sciences, William Vickrey, began studying private value auctions, in which bidders attribute a subjective value to the item. An example can be a dinner with a celebrity. There is no objective price that such a treat should have, as somebody who dislikes the celebrity in questions would not go to dinner with them even if it were for free. Conversely, common value auctions are such that the value of the item is the same for all bidders, but they have different signals about it.

Vickrey’s paramount contribution was the revenue equivalence theorem. All of the auction types that we have described above feature specific game theoretic strategies that players (bidders) should follow to maximize their utility (i.e. to get the item without spending more than what they value it). Vickrey showed that, if all bidders follow those strategies and are risk neutral, all of the formats presented above will result in the same revenue for the seller.

What was the two laureates’ contributions to the field?

The year is 1959. The Unites States Federal Communication Commission (FCC) allocates radio spectrum by evaluating companies’ application. The famous economist Ronald Coase (you might have heard of him in your micro 101 course) comes up with a revolutionary and – at the time – controversial idea, namely that the FCC should auction the spectrum. The rationale was that this process would save the government time, as it would not need to review applications, but even more importantly, it would drastically increase the revenue generated by spectrum sales by giving the contract to the highest bidder.

Fast forward to the Nineties. In 1994, John Nash wins the Nobel Prize for his enormous contributions to game theory. His field is in vogue. On February 13, 1995, the Wall Street Journal titles “Game theory is hot”. Precisely in those years, the powerful mathematical tool finds its most practical application in auctions. The FCC has finally accepted Professor Coase’s suggestion and set out to auction the spectrum. One of the teams working on the project is composed of (you guessed it) Paul Milgrom and Bob Wilson, who served as consultants for a company named Pacific Telesis. How did they get there?

In the Eighties, both Wilson and Milgrom published a series of influential papers (some of them with Stanford game theorist Prof. David M. Kreps, who for some reason was not awarded the Nobel prize with them) that built upon the foundations of auction theory and effectively turned it into a prosperous and widely applied field of research in microeconomic theory. They investigated both important theoretical questions, such as the strategic behavior of bidders in different auction formats, and practical issues like auction design for governments and regulators needing to achieve welfare maximizing results.

More specifically, Professor Wilson pioneered the theory of common value auctions, proving that Vickrey’s revenue equivalence theorem breaks in this setting. In fact, in common value auctions, bidders have imperfect information and signals regarding the item’s value, and therefore the winner will seek to bid below their best estimate. That happens because she anticipates that for her to win, she must bid higher than the other participants in the auctions. But if she bid higher than everybody else, she suspects that she might have valued the item more than what it is actually worth. Thus, she ends up bidding lower than her best estimate, in an effort to avoid the so-called winner’s curse.

Professor Milgrom’s foremost contribution to the field was, instead, on auctions that have both a common and a private value. A straightforward example is buying a house at an auction. In that situation, bidders will have their own taste, determining their private valuation of the house, but they will also keep in mind that the house is an investment, and surely they would not want to pay more than the common value for it. Moreover, Milgrom studied extensively the relationship between revenue and information.

Today, the two laureates’ work is not only the foundation of a stream of subsequent advancements in auction theory and game theory, but also the theoretical basis used to design auctions for the sale of sophisticated public goods and services in a way that is welfare maximizing and, thus, beneficial to society.

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The cover image is an artwork by Niklas Elmehed © Nobel Media.