Auction Theory From The Nobel Prize for Economics: Explained

In the dead of night, a phone call from one of the most elite institutions in the world goes unanswered by a Stanford professor. His partner rushes to inform him of an unexpected and momentous event. Paul Milgrom receives the word, in the early hours of Monday, while he was asleep with his mobile unavailable, from fellow professor Robert Wilson, still in his slippers, outside that they have managed what few could even dream of - winning the Nobel Memorial Prize in Economics.



The most prestigious academic award in the world has just been awarded to game theory economists Paul Milgrom and Robert Wilson of Stanford University, for their revolutionary work in the field of auctions, forever altering its landscape.


From pokemon cards sold on eBay to the high-flying world of million-dollar art pieces, auctions are present everywhere, with jaw-dropping amounts of money exchanged between buyers and sellers across the world each year.


Auctions, however, seem to be one of the simplest economic interactions governing these exchanges. In an auction, bidders bid against one another in increasingly large amounts, until the product can be sold for the most expensive price, maximizing the total utility for both buyers and sellers, the sole purpose of any auction.


However, in real-world auctions, it becomes far more complex and leaves room for improvement for both buyers and sellers. In fact, it has been shown time and time again that bidders often tend to bid less than their own estimate of the product’s worth, otherwise known as the winner’s curse.



Buyers are too afraid of overbidding and losing out on potential value in the future and accordingly decrease their bidding amounts. This causes items at auction to be frequently sold at less than their true value and not to the buyer that could have best taken advantage of the product's value.


Thankfully, Dr. Milgrom, with the help of Dr. Wilson, was able to create a new, more robust form for auctions, employed by institutions from the likes of Google to powerful national governments. The revolutionary auction form rests on the theory of common value and private values. In common value auctions, the value of the item is uniform across all bidders; however, each bidder has their own independent private value that is assembled based on their own assumptions, preferences, and available information.


A classic example of this is an auction for an unknown amount of quarters in a jar. The total value of the jar is identical among all bidders, but each bidder places varying private values of bids on the jar, depending on their own personal belief as to how much money they believe is in the jar. Thus, the winner’s curse could be in full effect causing bidders to overestimate the value within the jar causing the highest bidder to vastly overpay for the jar.



On the other side of the coin, the fear of succumbing to the winner's curse is in full effect, leading bidders to place bids lower than their own best estimates, in fears of overbidding and promptly losing money. Unfortunately, there are real world effects of this inefficiency, leading to less than ideal outcomes across a variety of different auctions, such as pollution rights and initial public offerings.


In order to minimize the effects, Wilson and Milgrom proposed providing as much information as possible to the bidders, so they can make an informed decision, making them less susceptible to fears of overpaying for the item. This information comes from two different sources. The seller should provide as much information about the item as possible, such as having an appraisal done by an expert.


Second, the auction must also be formatted in a way that bidders know the interests of their competitors, making last-minute winning bids impossible, that could otherwise undermine the competitiveness of the auction, causing inefficiency.


The real-world applications of Milgroms’s and Wilson’s research have been tremendous. Perhaps one of its most important applications is its involvement in how the US government sells radio frequencies. Previously, when deciding which companies get which licenses for which frequencies, the US government employed a method of a “beauty contest” where companies presented their cases for owning a specific radio frequency, leading to massive amounts of lobbying, that left potential millions unearned.


Milgrom and Wilson were able to greatly increase the utility for both the US government and the buyers. They proposed the elimination of the beauty contest, instead suggesting that the government distribute radio frequencies in a simultaneous multi-round auction.


In this auction structure, to avoid speculators from buying and reselling frequencies at a profit, the government sold radio frequencies in all geographic parts of the US at the same time. In addition, there are multiple rounds within the auction and bidders will be able to discreetly bid on frequencies they want. Then after each round of bidding, the top bids are then revealed for each frequency and the bidders can then choose to exit or raise their bids, repeated until only one bidder remains.


This revolutionary format allows bidders to bypass the winner’s curse because they know with 100% certainty that if they win, they can have a complete collection of all radio frequencies in the geographical region they want, without needing the extra cost of buying a frequency from a speculator to complete their collection.


Furthermore, by allowing buyers to still see the bids of their competitors it eliminates fears that they would be overpaying for the frequencies. Through this change, the federal government was able to increase the revenue by over $600 million, and the radio frequencies were better allocated among buyers, allowing buyers to buy radio frequencies that would truly allow them to provide a real service and make a profit off it.


From radio frequencies to pollution rights, and even air landing trackpads, the positive implications of Dr. Milgrom and Dr. Wilson’s work stretched far and wide, benefiting the government in increased revenue and allocating scarce resources to the most worthy buyers.


As the Nobel committee summarizes,

“the Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel 2020 was awarded jointly to Paul R. Milgrom and Robert B. Wilson for improvements to auction theory and inventions of new auction formats."

Written by Runzhe Cui


References

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