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?

(In reply to re(3): Solution by Lewis)

No, because once the second person bids, the first person loses money unless someone else bids, so if no one else bids, he will bid. Consider:
A) He bids 1¢. If there are no other bids, he gains 99¢
B) Bidder 2 bids 2¢. Bidder 1 will lose 1¢, so...
C) He bids 3¢ and stands to gain 97¢.

But then by the same reasoning, ...
D) Bidder 2 bids 4¢, and so on. The bidding war has begun.

A second bid does not "risk" a bidding war, it guarantees one!

Since everyone can think it through, they all realize that
the best position is to be the first to bid, and the second best, if they are too slow for the best, is not to bid. If there can be only one bid, it might as well be for the least permissible amount.

Posted by TomM on 2003-06-07 09:21:30