(FORTUNE Magazine) – Ever since game theory was invented half a century ago, people have been prophesying that it was about to revolutionize economics and management. It's easy to see why. One definition of it--the study of rational behavior in situations involving interdependence--seems to embrace the whole economy, and business in particular. The stuff of game theory--competition, cooperation, oligopoly, risk, uncertainty--is the very guts of managerial decision-making. But instead of fomenting revolution, game theory long seemed a great underachiever among social science ideas. It required too many simplifying assumptions to be of much practical use and remained an intellectual backwater, avoided as too abstract and arcane even by economists.

All that has changed over the past dozen years. Game theory at long last has begun to deliver the goods, in theory and in practice. One sign was the awarding of the 1994 Nobel Prize in economics to a trio of game theorists: Americans John Nash and John Harsanyi and German Reinhard Selten. Their collective accomplishment had been to work out the limitations and make game theory applicable to real-life situations. Only once their work had been completed--not until the early 1980s--could the revolution really begin.

The most dramatic example of game theory's new power has been unfolding since last summer in Washington, D.C., where the Federal Communications Commission is auctioning off wavelengths of the radio spectrum for such things as pagers and pocket telephones. Congress in 1993 ordered the agency to auction new spec trum licenses instead of giving them away as it had in the past. Exactly how to auction the licenses was not obvious. No one had any idea what they were worth, and to complicate things further, the value of any license depended on the other licenses a bidder could get. If you are bidding for the rights to offer pocket phone service in Connecticut and New Jersey, what you're willing to pay will depend quite a bit on whether you can get the license for New York City. There were also cautionary tales about auction fiascoes in other nations. New Zealand, for instance, picked a faulty auction design in 1990 that allowed a company that had bid 100,000 New Zealand dollars for a license to walk away with it for $6.

One of the first advances of the new game theory in the 1980s had been in the study of auctions, and it was to leading theorists in this field that Evan Kwerel, a senior economist at the FCC, turned for help in designing the spectrum auctions. What the boffins came up with was a "simultaneous multiple-round auction," where all the licenses of a particular type go on sale together and bidders may, with some limitations, bid for any collection of licenses until bidding stops. Theory said this would help the bidders arrive at the right prices, would award the licenses to the companies that would use them efficiently, and would produce the most revenue.

The first auction under these rules was last July, for narrow-band personal communications services, such as pagers. It was a triumph, not only for the FCC and the taxpayers--it raised $617 million--but also for game theory (and game theorists, hired in droves as consultants by bidding companies). "Economists finally got their way and witnessed the wisdom of their recommendations," crows Peter C. Cramton, an associate professor at the University of Maryland. As the chart shows, faint-hearted bidders quickly dropped out. The total value of the licenses became apparent only when new bids stopped. The big daddy of the FCC spectrum auctions, the sale of broadband licenses for the next generation of wireless phones, began December 5 under similar rules and is expected to raise billions when bidding ends early this year.

Auction theory will spin off practical applications for business as well. A company planning to divest several divisions or subsidiaries, for instance, faces a problem like the FCC's: Letting potential bidders express their preferences for different aggregations of the assets may be more efficient than for the seller to make the decision. Modern game theory can also help managers think about any number of strategic problems. The textbooks tend to be jargon-intensive and mathematically challenging. A classic introduction for the general reader is John McDonald's Strategy in Poker, Business, and War, and the most user-friendly guide for businesspeople is John McMillan's Games, Strategies and Managers (Oxford University Press).