The price of virtue

You might think that a "dollar auction" is just a more expensive penny auction, but it isn't, not exactly. The dollar auction was a parlor game invented by the economist Martin Shubik, working with John Nash, the crazy guy from A Beautiful Mind. It was a standard auction, except you paid whether you won or not. (The "merchandise" being auctioned off was a dollar bill, whence the name.)

When the auction was a nickel or so, the bidders thought they were getting a great deal and so they didn't drop out. And then as the bid-level approached "par" (what the merchandise was worth; in this case, a dollar), the bidders would start to realize that winning wasn't going to be such a great deal, but that losing would really suck. If the bidding stopped at 99¢, the winner only made one cent, but the the loser would lose 98¢! Once you started bidding, it was always in your interest to bid one more time.

Shubik wrote later, "Experience with the game has shown that it is possible to 'sell' a dollar bill for considerably more than a dollar. A total of payments between three and five dollars is not uncommon."

The part that interests me is not why the auction doesn't stop sooner (that's amusing, but not complicated), but why it stops at all. If there's an auction between Bob and Sam and the auction is hammered down in Bob's favor at $5.00, Sam must have just decided to lose $4.99, instead of making one more bid and "winning", thereby losing only $4.01 (since he would pay $5.01, but get a dollar as the prize).

Why did Sam do that, why did he walk away? What changed about the auction between the point where the bidding was at 50¢ and the point he finally quit?

Well, for one thing, Sam realized he was screwed. He had belatedly grasped the economics of the auction and decided to step off the merry-go-round. Of course, he could have achieved the same effect at less cost by just thinking through the consequences before he started, he just didn't. (There's an old saying that "Experience is the harshest teacher but a fool will have no other.")

But Sam learned something else, something he could have only learned from participating in the auction: he learned just how stupid and stubborn his opponent Bob was. Bob demonstrated that he was willing to lose any amount of money just in order to "win". Sam was wise enough to realize that fact and flexible enough to act on the realization. Sam's reward for the virtues of wisdom and flexibility was: he lost.