Milgrom & Wilson (2020): The Science of Selling Things Nobody Knows the Value Of

Why Auctions Are Hard

Auctions seem simple: people bid, the highest bidder wins. What’s there to study?

Everything, it turns out. An auction is a situation where nobody knows the right price. The seller doesn’t know how much buyers are willing to pay. Buyers don’t know how much the item is truly worth — or how much other buyers are willing to pay. The auction format itself — who bids when, what information is revealed, how the winner pays — shapes the outcome in profound ways.

Get the design wrong, and sellers leave money on the table. Bidders overpay and regret it. Resources go to the wrong people. Get the design right, and auctions become one of the most powerful tools for allocating scarce resources efficiently.

Paul Milgrom and Robert Wilson didn’t just study auctions — they reinvented them. Their theoretical breakthroughs explained why bidders behave the way they do, and their practical inventions created entirely new auction formats that governments now use to allocate billions of dollars’ worth of public resources.

Wilson: The Winner’s Curse and Common Values

Before Wilson’s work in the 1960s and 1970s, auction theory focused on private values — situations where each bidder knows exactly how much the item is worth to them personally. You’re bidding on a painting you love; your value depends on your taste, not anyone else’s.

But many important auctions involve common values — the item is worth roughly the same to everyone, but nobody knows exactly what that value is. Consider:

• Oil drilling rights: The oil under the ground is worth the same to any company that extracts it. But nobody knows exactly how much oil is there
• Treasury bonds: A government bond pays the same interest to whoever holds it. But its future market value is uncertain
• Radio spectrum: A frequency band has a market value that depends on how many customers will use it — unknown to all bidders

Wilson developed the first rigorous theory of common-value auctions and identified the winner’s curse: the tendency for the winning bidder to overpay.

The logic of the curse:

• You’re bidding on oil drilling rights along with nine other companies. Each company has its own geological estimate of how much oil is underground
• The estimates are scattered around the true value — some too high, some too low
• The company with the highest estimate wins the auction. But the highest estimate is almost certainly an overestimate. The winner is the company that was most wrong — in the optimistic direction
• Rational bidders who understand this will shade their bids downward — bidding less than their estimate to avoid the curse
• But how much to shade? Wilson’s theory provided the answer, showing exactly how rational bidders should adjust for the number of competitors, the degree of uncertainty, and the auction format

Wilson showed that the winner’s curse is worse when:

• There are more bidders (more chances for someone to have an extreme overestimate)
• Uncertainty is greater (estimates are more dispersed)
• Some bidders have better information than others (the informed bidder wins when the item is worth more; the uninformed bidder wins when it’s worth less — a devastating asymmetry)

Milgrom: A Unified Theory of Auctions

Milgrom’s breakthrough was recognizing that most real auctions involve both common and private values simultaneously.

Consider a telecom company bidding for radio spectrum:

• Common value: The spectrum’s market value depends on population density, technology trends, and consumer demand — roughly the same for all bidders
• Private value: The spectrum’s value to this specific company depends on its existing network, technology, and business strategy — different for each bidder

Milgrom built a general framework that encompassed both pure private values and pure common values as special cases, with most real auctions falling somewhere in between.

Key results:

• The linkage principle: Auctions that reveal more information during the bidding process generate higher revenue for the seller. Why? Because information reduces the winner’s curse, allowing bidders to bid more aggressively. An open ascending auction (where you can see others’ bids) outperforms a sealed-bid auction because each round of bidding reveals information about others’ estimates
• English auctions beat Dutch auctions: In an English auction (price rises until one bidder remains), bidders learn about others’ valuations as competitors drop out. In a Dutch auction (price falls until someone bids), no information is revealed. For common-value items, English auctions produce higher revenue
• Revenue ranking of auction formats: Milgrom showed that the four standard auction formats — English, Dutch, first-price sealed-bid, and second-price sealed-bid — generate different revenues depending on the mix of common and private values. This gave sellers a principled basis for choosing the right format
• Information asymmetry matters enormously: When one bidder has better information (an “insider”), other bidders bid cautiously, and the seller’s revenue drops. The solution: make the insider’s information public, or use an auction format that reveals more information during bidding

The Spectrum Auction: Theory Becomes Practice

In the early 1990s, the U.S. Federal Communications Commission faced a practical crisis. Mobile phone use was exploding, and the FCC needed to allocate radio spectrum to telecom companies. Previous methods — administrative hearings and lotteries — were slow, arbitrary, and left billions of dollars on the table.

Congress mandated that the FCC use auctions. But no existing auction format could handle the problem:

• Thousands of licenses across different geographic regions needed to be sold simultaneously
• Licenses are complementary: A license for New York is worth more to a company that also has New Jersey, because customers cross state lines. Bidders need to assemble packages of licenses — but they don’t know if they’ll win the neighboring licenses they need
• The exposure problem: If you bid high for New York expecting to also get New Jersey, but lose New Jersey, you’re stuck overpaying for New York alone. This risk discourages bidding
• Diverse bidders: Large national carriers and small regional operators have very different needs and resources

Milgrom and Wilson designed the Simultaneous Multiple Round Auction (SMRA):

• All licenses offered simultaneously: Instead of selling licenses one at a time (which makes it impossible to assemble packages), all licenses are on the table at once
• Multiple rounds of bidding: Prices start low and rise gradually. After each round, all bids are revealed. This gives bidders information about others’ valuations — exploiting the linkage principle
• Activity rules: Bidders must be actively bidding in each round — no sitting on the sidelines waiting. This keeps the auction moving and prevents strategic delay
• Withdrawal penalties: Bidders can withdraw a bid, but must pay a penalty. This prevents manipulation while allowing some flexibility

The first SMRA auction in 1994 sold 10 licenses over 47 rounds, raising $617 million. The *New York Times* called it "the greatest auction ever." Subsequent U.S. spectrum auctions have raised over$100 billion.

Later innovations by Milgrom:

• Combinatorial Clock Auction: Allows bidders to bid on packages of licenses directly, rather than assembling packages through individual bids. This solves the exposure problem but requires significant computational power
• Incentive Auction (2016): A two-sided auction that first buys spectrum from TV broadcasters (reverse auction) and then sells it to wireless companies (forward auction). This repurposed 70 MHz of spectrum for mobile broadband, raising $19.8 billion — the largest spectrum auction ever

Why Auction Design Matters

The spectrum auction is the most visible application, but auction theory has transformed how society allocates resources far beyond radio frequencies:

• Electricity markets: Power generators bid to supply electricity, and the auction format determines both efficiency and prices for consumers
• Carbon emissions: Cap-and-trade systems use auctions to allocate pollution permits — the design determines whether emissions reductions happen at least cost
• Government procurement: When governments buy everything from office supplies to military equipment, auction design determines whether taxpayers get good value
• Online advertising: Every Google search triggers an auction among advertisers for the ad slots on the results page — billions of these auctions happen daily
• Treasury securities: Governments sell bonds through auctions; the format affects the interest rate taxpayers pay on national debt

The SMRA format has been adopted by 97 countries for spectrum allocation, with approximately 15,000 licenses awarded through 420 auctions worldwide.

Their 2020 Nobel Prize was awarded “for improvements to auction theory and inventions of new auction formats.” As the Academy noted: “The new auction formats are a beautiful example of how basic research can subsequently generate inventions that benefit society.”

Explain It to a Child

Imagine you and your friends find a jar full of coins, but you can’t open it to count them. Everyone guesses how many coins are inside, and whoever guesses the highest gets to buy the jar for that price. Here’s the problem: the person who guesses highest is probably guessing too high — they’ll pay more than the jar is worth. That’s the “winner’s curse,” and Wilson figured out how smart bidders can avoid it. Now imagine something harder: the government wants to sell phone companies the right to send signals in different areas — like selling invisible patches of sky. A phone company wants a patch over New York AND New Jersey together (because phone calls cross borders), but if they only get one, it’s not worth as much. Milgrom and Wilson invented a new kind of auction where all the patches are sold at the same time, with many rounds of bidding, so companies can see what others are doing and adjust. Their auction raised billions of dollars and is now used all around the world.