What has been the most single exciting province of applied economics these last dozen years?  Auction engineering, probably. What developments in finance were to the '60s and '70s, auction theory was to the late '70s and '80s. And when the '90s came along, economists were ready.

It wasn't just the nations of the former Soviet Union and its Eastern European satellites that needed to sell off state-owned assets. The tendency to perestroika, privatization and deregulation was world-wide.

In the industrial democracies, new technology was rendering obsolete the old regulatory apparatus, in which rights were distributed free to applicants deemed deserving and trustworthy.  In 1982, the demand for cellular phone licenses overwhelmed the system. A lottery was adopted, creating a scramble among well-heeled speculators as unjust as it was wasteful. At one point, a group of Cape Cod dentists entered the competition for the right to operate a local cellular telephone business. They won, and promptly sold their license to a real telephone company for $41 million. Government clearly was leaving far too much money on the table.

So in 1994, the Federal Communications Commission hired Stanford University's Paul Milgrom and Robert Wilson to design an auction to sell off rights to a portion of the electromagnetic spectrum in the United States. After 47 rounds of electronic bidding on untested software over five days, the procedure was deemed a remarkable success -- ten licenses for paging services, a sliver of the spectrum, sold for $617 million. The auction set an international standard for the sale of publicly-owned resources.

The FCC is currently preparing to sell 1,100 wireless spectrum licenses at auction in August. The state of Illinois plans to buy a couple of years' worth of spare electricity for its two biggest utilities at a falling-price (or "clock") auction in September. The European carbon-trading system is on the verge of collapse, but carbon dioxide emission auctions are in the works to save it. Real estate; mineral and resources rights; going businesses; seats on airplanes; the services of newly-graduated medical interns; and, of course, all manner of goods on eBay, are routinely sold at auction.

Such transactions have become so common that it is difficult to remember that just a dozen years ago, until the first big FCC auction demonstrated that they could be made to work for governments, they were rare.

An abundant literature has grown up to describe these developments.  Reed Hundt was the FCC chairman who set in motion the spectrum auctions; his You Say You Want a Revolution: a Story of Information Age Politics affords an account of the politics of the decade during which the Internet rolled out. John McMillan was the expert the FCC hired as a consultant; Reinventing the Bazaar: a Natural History of Markets is the best general overview of the world-wide turn to markets. Paul Klemperer, architect of a major British spectrum auction, has written a non-technical bookon auction design, and Vijay Krishna, an introductory text. Robert Hall's Digital Dealing: How e-Markets Are Transforming the Economy is a primer for those seeking to understand the new deal engines, from eBay to Orbitz to Nasdaq.

But for a certain kind of reader, none is better than Paul Milgrom's Putting Auction Theory to Work. Seven of its eight chapters consist of formal exposition of auction theory. But Milgrom's first chapter, and the foreward to the book by Evan Kwerel, can be read with interest by anyone curious to understand how revolutions in public policy come about.

A willingness to act swiftly on spectrum auctions was one of the initiatives that Bill Clinton brought with him to office. (Vice President Al Gore arranged the appointment of his high school friend Hundt to the FCC.) Congress authorized the practice in August 1993, requiring that the first auction be held within a year. It was Kwerel who, as head of the FCC's Office of Plans and Policy, was assigned the task.  

An MIT PhD, Kwerel had been an enthusiast of auction schemes since he joined the staff in 1983. Milgrom and Wilson (professors working as consultants to Pacific Bell) and Preston McAfee (working for AirTouch), had changed Kwerel's thinking about the possibilities for running an ascending-bid auction in multiple stages.  Such a mechanism would raise the greatest possible amount of money from those who would operate the broadcasting businesses, without stimulating the exuberant tendency to pay too much that produces "winner's curse."

But could a complex system be created in the short period of time specified by Congress? Once begun, would the reiterative process specified by the rules ever end? The safe alternatives available to the FCC were the familiar practices of open-outcry auction or sealed bids. But neither mechanism offered anything like the new high-tech system for eliciting information from bidders on the highly interdependent values of spectrum goods, or reducing bidders' opportunities to game the system. And whatever mechanism was adopted would become the standard for future auctions.

Kwerel describes the intense effort that went into the project: Karen Wrege, the veteran manager recruited from the Resolution Trust Corporation (where she had been selling off the assets of bankrupt savings and loan associations),  who found a way to visualize the auction, thereby convincing Hundt that it would really work; the Caltech team (led by experimentalist Charlie Plott) hired to torture test the auction software, which offered students fat prizes to find the bugs; the complete system failure that occurred the night before Auction #3, and the steely courage required to bring it back to life; the race to complete the auction before the ballroom of Washington's Shoreham hotel had to be turned over to a wedding party.

For his part, Milgrom concentrates on laying out the basic concepts necessary for understanding an auction for a complicated wireless market -- substitutes and complements, ascending and descending auctions, second price and highest-rejected-bid rules. He gives special attention to the cautionary tale of New Zealand's pioneering radio spectrum rights auction in 1990, which ended in embarrassment. 

Following its consultant's advice, the New Zedders adopted a second-price sealed bid auction, adopting a mechanism originally proposed by Columbia University professor William Vickrey in 1961 to discourage the "shading" (or low-balling) of bids.

In a Vickrey auction, the highest bidder get the prize, but pays a price equal only to the second-highest bid in the auction -- a rule designed to simplify strategic considerations among the bidders, each of whom will bid the highest price they are willing to pay, without having to be present physically or guess others' behavior. (An especially lucid explanation of how this honesty-is-the-best-policy rule is supposed to work can be found here.)

But the rules New Zealand adopted overlooked completely that matter of interdependence, Milgrom notes -- the issue of whether some licenses might be substitutes for one another and others be complements (that is, more valuable when owned in combination. That introduced an element of pervasive uncertainty and myriad opportunities for low-ball strategies, for shying away from some licenses and overbidding on others. The result was anything but efficient. The auction had been expected to raise around NZ$250 million. Instead it netted NZ$36 million. One firm bid NZ$100,000 for a license, and paid the second-highest price of only NZ$6.

Milgrom's design for the FCC auction improved on the New Zealand mechanism in a number of ways, mostly by improving transparency. He established eligibility and activity rules. He mandated that all licenses be sold at once, in a single open ascending auction, such that bidders could place bids on any and track bids on all. Sound complicated?  It was. But when it was finished, the world had a new electronic auction system, capable of apparently endless refinement and variation.

 Such was the excitement that, a year later, the auction community persuaded the Swedish Academy of Sciences to recognize William Vickrey's original achievement (and some related work on asymmetric information by James Mirrlees) with a Nobel Prize. (The 82-year-old Vickrey died of a heart attack before he could accept the award; Jean-Jacques Laffont gave the Nobel lecture in his stead.)

When Milgrom's book appeared two years ago, the Institute for Advanced Study's Eric Maskin, a leading auction theorist himself, wrote in the Journal of Economic Literature, "By any standard measure, auction theory has been an enormous success.  Even after 25 years of intensive work, the literature continues to grow at a prodigious, even accelerating pace; it has spawned much empirical and experimental work; its tentacles have spread into other disciplines [computer science, in particular, where the focus is on computational issues]; and auction theorists has been influential in the design of mechanisms for the privatization of public assets (such as spectrum band) and for the allocation of electricity and other goods (they have also served as consultants to the bidders in those mechanism)."

Milgrom had played a starring role, wrote Maskin. The book had been eagerly awaited ever since 1995, when it was first presented in a series of lectures. It did not disappoint.  It was Milgrom's master-class, a demonstration of the fundamental unity of auction theory and an exhibition of its beauty. Hen added, "Economists, being a hard-boiled lot, sometimes deny that esthetics have anything to do with what they are up to. But this sentiment belies the fact that the most important economic ideas, e.g. the first welfare theorem of competitive theory or the principle of comparative advantage, are things of real beauty."

In fact, Maskin continued, "...some of Milgrom's observations about auctions in practice are a good deal less compelling that the book's theoretical results. But this contrast is not primarily his fault. In spite of all that it has accomplished, auction theory still has not developed far enough to be directly applicable to situations as complex as, say, the spectrum auctions." Giving advice on auctions, according to Maskin, "is far less a science than an art. And the essence of an art is far harder than a science to convey convincingly in writing."

Which makes it, of course, an even more interesting story!