Sometimes the main contribution of game theory to auction design is not some deep theorem but simply the idea that it is vital for auction designers and bidders to put themselves into the minds of their opponents. In recent years several disastrous auctions have shown that when an auction is poorly designed, bidders will exploit the rules in ways the auction’s creators didn’t anticipate.

For instance, in 2000, Turkey auctioned two telecom licenses one after another, with the stipulation that the selling price of the first license would be the reserve price for the second license—the minimum price they would accept for it. One company bid an enormous price for the first license, figuring that no one would be willing to pay that much for the second license, which did in fact go unsold. The company thus gained a monopoly, making its license very valuable indeed.

Sometimes bidders find sneaky ways to encode messages in their bids. In 1999 Germany sold 10 blocks of spectrum in an English auction with just two powerhouse bidders: Mannesman and T-Mobile. The auction rules stated that bidders placing new bids always had to raise the current high bid by at least 10 percent. In the first round Mannesman bid 18.18 million Deutsch marks per unit on blocks 1-5 and 20 million on blocks 6-10. T-Mobile noticed, as did many observers, that adding 10 percent to 18.18 million brings it almost exactly to 20 million. T-Mobile read Mannesman’s bid to mean, “If you raise our bid on blocks 1-5 to 20 million and leave blocks 6-10 for us, we won’t get into a bidding war with you.” T-Mobile did just that, and the two companies happily divided the spoils.

Figuring out how to prevent such abuses is keeping auction theorists busy. And many other, more specific questions about auction design remain unanswered. Some auction theorists, such as Lawrence Ausubel of the University of Maryland, College Park, are trying to understand how to structure auctions in which many identical items are being sold, to prevent bidders from keeping prices low simply by reducing their demand. Others, such as Paul Klemperer of Oxford University, who helped design the hugely successful British spectrum auction of 2000, are tackling the question of designing auctions with few potential bidders, with the aim of attracting as many competitors into the bidding as possible. A disastrous spectrum auction in November 2000 in Switzerland, in which exactly four strong bidders were bidding for four licenses in an open English auction, highlighted the importance of this problem. Not surprisingly, the bidders got the licenses for a steal, paying less than one-thirtieth the price companies had paid for similar licenses in Britain and Germany just months earlier.

The United States electromagnetic spectrum auctions have given theorists something new to mull over: package bidding. Designing auction rules so that a company can place a single bid for a package consisting of both the northern and southern California licenses would eliminate the chance of the firm getting stuck with one and not the other. This would allow bidders to form more efficient bundles of licenses and make them bid more confidently (and hopefully, higher). But running an auction with package bidding is immensely complicated. If the buyers are all bidding on different packages, how does the auctioneer even decide which are the highest bids in each round? These are thorny issues, but auction theorists are starting to make headway. Milgrom and Ausubel have been working with the FCC to develop package auction designs, and the FCC plans to run a package auction in the near future.

With the advent of online auction services such as eBay, auctions have made their way not only into multi-billion-dollar government sales but also into the daily lives of ordinary people. Observations of these auctions are generating fresh questions. Why, for instance, do many eBay bidders wait until the final seconds of an auction before bidding?

Problems such as these are giving auction theorists a wealth of fascinating new puzzles to sharpen their insight. They will be able to draw upon the wealth of basic research into game theory and its application to auctions. The founders of game theory would surely have approved. Figuring out ingenious strategies and counter-strategies is, after all, the name of the game.