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 Solution???? by Jonny Doe)

Bidding one dollar for a buck at this auction is a disasterous tactic. Suppose the high bid before you was 90¢. Now that you bid a dollar, if the bidding stopped right now that person would be out the 90¢, since the first and second highest bidders have to pay. Knowing this, that person would probably outbid you, bidding perhaps $1.25, figuring it is better to win the buck and be out only 25¢ than it is to lose 90¢.

Now you will lose your dollar, unless you outbid the other bidder, in which case this scenario gets worse and worse. As each of you outbids the other in an effort to minimize your loss, your money at stake (and potential loss) goes up and up, which is exactly what the auctioneer wanted in the first place.

If you could collude with the other bidders to stop the bidding below 50¢ and split the buck, you could collectively make a profit. Obviously, this would be maximized if there were only one bid of 1¢ and the bidding stopped there. In all likelihood, however, someone in the group of bidders would forget the rules and outbid you, and as soon as the bidding gets above 50¢ it will most likely snowball to several dollars using the reasoning stated above.

As Joshua (the WOPR) declared in War Games,

AN INTERESTING GAME, PROFESSOR
THE ONLY WINNING MOVE IS
NOT TO PLAY

HOW ABOUT A NICE GAME OF CHESS?

Posted by Bryan on 2003-06-03 05:07:54