I have a one dollar bill. there is a crowd of people around me. I hold it up and say that i will auction the one dollar bill off, and the dollar would go to the highest bidder.

The catch? the first AND second highest bidder both have to pay me whatever they bid. For example, if the bidding stops when someone bids 1.00 and the next person bids .95, then I get 1.95, and the winner gets nothing, the second person loses 95 cents.

What would you do if you were at this auction, and there had to be at least one bid? What is the "winning" strategy, assuming that everyone will want to do what is best for them?

OK.

First, the puzzle posits that everyone thinks logically (and knows all the others do, too). This does not match the real world, but is common in puzzles, just as Knights and Liars are not real world figures.

Second, everyone wishes to maximize their winnings and minimize their losses. They will bid as low as possible, and will not bid if a bidding war is inevitable.(But see the third point.)

Third, there has to be at least one bid.

Notice that no matter how low he bids, the first bidder is out money if a second bid is the last bid. Even if no one else makes the third bid, he has to (to recoup his losses) and the bidding war begins.

Since each of the others know this, they will not make the second bid. (See my second point, above.)

So the winning strategy is to make the first bid. And since no one will outbid you, make that bid as low as possible: 1 cent.

Posted by TomM on 2003-06-07 00:49:00