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Two Stanford economists – Paul Milgrom and Robert Wilson – were awarded this year’s Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel “for improvements to auction theory and inventions of new auction formats”. Their work has many applications, ranging from pricing government bonds to licensing radio-spectrum bands in telecommunications.
An auction is usually a process of buying and selling goods or services – by selling the item to the highest bidder. Millions of young people of the country would think about the IPL player auction first when they’ll hear the word ‘auction’. However, the auction is a well-established license assignment tool in the modern world – possibly the most widely used method in today’s world to lease/sell the rights of mines, coal blocks, electromagnetic spectrum, railways, airports, and what not. Theoretically, it’s an important part of modern game theory. However, the theory largely relies on identifying the driving forces in bids of the bidders.
Three very standard ways of auctions are ‘English auctions’, ‘Sealed bid auctions’ and ‘Dutch auctions’. In English auctions, bidders bid openly against each other and the bids continue to increase. Ultimately, the object is sold to the highest bidder. In a sealed bid auction, bidders bid privately, and again the object is sold to the highest bidder. In a Dutch auction, however, the price on an item is lowered until it gets a bid. The item is sold to the first bidder to accept that price, assuming that the price is above the reserve price.
If three individuals – P, Q and R – are up for buying an object and all are willing to pay Rs 10,000 for that, all these three auction types will see someone buying the object at about Rs 10,000. However, if P is willing to pay Rs 20,000, Q is willing to bid Rs 10,000, and R don’t want to bid beyond Rs 5,000, P will win the object in all three types of auction. However, assuming Rs 100 being the increment, P will get it in Rs 10,100 in an English auction, but in Rs 20,000 in both sealed bid and Dutch auctions.
Canadian economist William Vickrey, who was awarded the Nobel Memorial Prize in Economic Sciences in 1996, was possibly the first person to explain auction by Game Theory. Vickrey described auction theory in a setup where one bidder’s bid is unrelated to the valuation of the item to other bidders. Vickrey’s theory essentially imply that the auction procedure does not matter whatever be the method of auction – Dutch auction or English auction or sealed bid.
Wilson and Milgrom disagreed. Robert Wilson proposed the idea of “common value” by developing a bidding model that reveals a mutually beneficial equilibrium outcome without the requirement of sharing information in advance between seller and buyers. A typical example maybe the case of bidding for the right to extract natural gas. Here the value of the object (gas) is a “common value” – at least to some extent, because the gas has to be sold at the global market price. Wilson wrote: “no bidder knows the true value of the item, yet it is essentially certain the seller will receive that value as the sale price.”
However, Wilson showed that there exists a tendency for the winning bid in an auction to exceed the true worth of an item, and thus it may induce “winner’s curse”. Sometimes the winner tend to overpay in order to buy an object, and that will be loss for the winner. The term “winner’s curse” was coined as a result of companies bidding for offshore oil drilling rights in the Gulf of Mexico.
Paul Milgrom went one step forward and argued that, in addition, there exists a “private value” for a product in each bidder’s mind. In fact, Milgrom incorporated both “common” and “private” values into a more general framework within the same model, and argued that revenues become higher when bidders can learn about each other’s bids. As the Nobel committee writes: “In most auctions, the bidders have both private and common values. … 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).”
The most fascinating and important aspect of Milgrom and Wilson’s achievement is that they tried to implement their theory by considering all possible practical issues. In early nineties, the telecom revolution was taking off. When, in August 1993, President Bill Clinton signed a historic law granting the US Federal Communications Commission (FCC) the authority to auction spectrum licenses, it paved the way of blending modern game theory into real life auctions and thus became a change-point in the history of modern auction.
In 1994, FCC used Milgrom and Wilson’s ideas in a “simultaneous ascending auction” by increasing information flows, which helped to maximise the value of public assets with great success. In fact, FCC was poised to sell a whole range of frequencies. In their simultaneous multiple-round auction, bidders are allowed to bid over several rounds of bidding, the bid-values being revealed at the end of each bid, which provide a chance to learn about others’ private information, and generate fairer and more efficient and profit-making outcomes.
Paul Milgrom’s 2003 book, Putting Auction Theory to Work, and a chapter entitled ‘The Greatest Auction in History’ in the 2010 book Living through Economics, provide an excellent description of this historic auction along with the underlying theories and backgrounds.
The FCC, however, was not ready to tolerate the auction extending indefinitely or for a long time through little bidding. Hence, the “standing high bid” for each license is posted at the end of each round along with the “minimum bids” for the next round. If the minimum increase is allowed to be too small, the auction could take too many rounds without much profit but causing serious administrative difficulties, whereas a too large amount of minimum increase would see inefficient allocation of the licenses and would incur serious loss. Minimum bids for the next round are computed by adding a pre-determined increment, which may be about 15% of the standing high bid in the early rounds, and 5% of the standing high bid in the late rounds.
The ‘closing rule’ suggested by Milgrom and Wilson was to end the auction after a round in which there will be no new bids on any license. The ‘activity rule’ indicates that a bidder placing eligible bids for a number of units at some round cannot bid for a larger number of units at any subsequent round. If a bidder is not active on a minimum percentage of units for which it is eligible to bid it loses the eligibility permanently.
Ten licenses were sold in 47 bidding rounds in $617 million in this FCC auction. The FCC auction was a grand success, indeed. In 1995, the New York Times columnist William Safire dubbed this 1994 FCC auction “the greatest auction in history”. There is little doubt that the foundation of Milgrom and Wilson’s Sveriges Riksbank Prize in 2020 was laid in that 1994 FCC auction. In fact, Milgrom and Wilson’s theory became the blueprint of many such influential auctions in the modern world.
Within just seven years of this FCC auction, Milgrom-Wilson’s designs had yielded sales totalling more than $100 billion in auctions worldwide. This was used in telecom licences in different countries. Milgrom also contributed designing electricity auction designs in New Jersey and Texas, asset sales in the US and Mexico, and also internet procurement auctions.
As economist Preston McAfee has said: “Unlike many theoreticians, Wilson and Milgrom brought their work to the real world, and transformed government policies toward auctions around the world.” Not many people apply their theory in practice in such vigour, and this may just be the true legacy of their contributions.
Atanu Biswas is a professor of statistics at the Indian Statistical Institute, Kolkata.