When I say ''old,'' I mean it. Herodotus described a Babylonian marriage market, circa 500 B.C., in which potential wives were auctioned off. Notably, some of the brides sold for a negative price.

The Romans used auctions for many purposes, including auctioning off the right to collect taxes. In A.D. 193, the Praetorian Guards even auctioned off the Roman empire itself!

We don't see auctions like this anymore (unless you count campaign finance practices), but auctions are used for just about everything else. Online, computer-managed auctions are cheap to run and have become increasingly popular. EBay is the most prominent example, but other, less well-known companies use similar technology.

DoveBid, for example, auctions off surplus industrial equipment. Excess machinery that would be rusting in back lots in Chicago can be put to use in Shanghai. Internet auctions facilitate these transactions, reducing waste and duplication.

The economist William Vickrey wrote the first major theoretical analysis of auctions in 1961 and received the Nobel for this work 35 years later.

Mr. Vickrey's work has been refined and extended by dozens of economists over the last 40 years. It is a beautiful and powerful theory, leading to several important insights that have had a large impact on auction design.

These days, when governments decide to auction off state-owned resources, they routinely hire economists for advice on how to design the auction. But bidders also hire economists to figure out how to beat the system.

Paul Klemperer, an Oxford economist, recently wrote a paper called ''What Really Matters in Auction Design,'' which includes many amusing, and sobering, stories of auction manipulation. This paper, and related materials, can be downloaded from his Web site at www.paul klemperer.org.

Mr. Klemperer argues that the principles of good auction design are the same as for any other market: try to encourage entry, and try to discourage collusion.

Ascending-bid auctions, particularly when they involve only a few bidders, are often susceptible to collusion, since participants can use early rounds to signal intentions.

In 1999, Germany sold some mobile-phone spectrum by auction, with one rule specifying that any new bid had to exceed the previous high bid by 10 percent. Two serious bidders were involved.

One company bid 18.18 million marks on blocks 1 to 5 and 20 million on blocks 6 to 10. Why the difference? Note that 18.18 million plus 10 percent is just about 20 million. The first company was sending the second a message: ''We think 20 million is the right price: let's not compete to push it up.'' The signaling strategy worked: the auction ended after two rounds, and each bidder got half the blocks at the same low price.

This is an example of an offer to compromise being encoded into the bids. Bidders can also encode a threat to punish. In the mid-1990's, two telephone companies were in a bidding war in a spectrum auction for Lot 378 in Rochester, Minn., generally bidding in round numbers. One company suddenly bid $313,378 and $62,378 on two other lots in Iowa that the second company thought it had won. The message there was also clear: stop bidding on Lot 378 or we will drive up the prices of other lots you really want.

It is hard to mount a legal challenge to this sort of behavior, particularly if there are no specific rules against it. Mr. Klemperer argues that a better way to avoid such ''implicit collusion'' is to require bidders to bid in round numbers, anonymously.

In addition to discouraging collusion, good auction design should also encourage entry. If everybody thinks a single strong bidder will win, it is hard to encourage others to enter. So, companies have a strong incentive to try to scare off potential competitors. Mr. Klemperer cites examples of public pronouncements of news releases and interviews that seemed intended to have this effect.

In November 2000, Switzerland was selling off four mobile-phone licenses but used an auction design that favored stronger companies, thereby discouraging entry. Furthermore, a week before the auction started, the nine likely bidders made a number of joint-bidding agreements, leaving just four coalitions bidding for four licenses.

Since there was no competition, the licenses sold at the minimum price set by the Swiss government, one-fiftieth of what had been expected.

There are many more fascinating stories. In an Australian sealed-bid auction for satellite television licenses, one company submitted several different bids on the same license and then, after winning, defaulted on the bids that were too high. It ended up paying a price only slightly higher than the amount bid by the next-highest bidder.

In 2000, Turkey auctioned two telecommunications licenses, with the rule that the minimum price for the second license was equal to the winning bid for the first. One company left itself with a highly profitable monopoly by bidding a very large price for the first license, rightly figuring that no one would be willing to pay that much for the second.

Mr. Klemperer emphasizes that auction design must be sensitive to the context. Are there a few dominant bidders or lots of potential entrants? Is this a one-shot or a repeated auction? Are there ways to signal intentions before the auction commences?

An appropriate design depends critically on the answers to questions like these.

One form that Mr. Klemperer particularly likes is the ''Anglo-Dutch auction.'' This uses an open, ascending-bid auction until only two bidders are left. These two then submit final sealed bids.

Auction designs like this may well help control manipulation. When a lot of money is at stake, every design will be probed for weaknesses, and attention to detail is critical.