Martin Shubik invented a famous game-theory exercise, sometimes called “the dollar auction,” where a teacher auctions off a $20 bill to the highest bidder. Bids have to be in round dollar amounts, but the twist is that both the highest and the second-highest bidder have to pay. When uninitiated students start to play this game, someone rushes to bid $3 or $4 dollars for the prospect of winning $20, and then other students respond by bidding up the price.
But then something amazing happens as the auction price starts approaching $20. The remaining bidders realize that they could end up having to pay a lot of money and not win the auction. Imagine that you had bid $19, and another bidder upped the ante by bidding $20. What would you do? Is it better to bid $21 for a $20 prize or to remain silent and pay $19 for nothing?
What starts off as a feel-good exercise to take advantage of a generous professorial offer suddenly becomes a sickening war of attrition, where the last two bidders pay more than what the prize is worth. These games routinely end with the winning bid being 50 percent higher than the value of the prize. Since both the highest and second-highest bidders pay, this means that the professor rakes in about three times the amount being auctioned.
This is an example of what auction theorists call an “all-pay” auction, and it’s a game you want to avoid playing if you possibly can.
But Barry Nalebuff pointed me toward a scary website — called swoopo.com — that seems to be exploiting the low-price allure of all-pay auctions. And it seems to be working.