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: Dollars and Sense by ryan smith)

I wouldn't bid $1.00 against an opening bid of $0.99. I have said that already. In fact I wouldn't bid against any opening bid. But, that doesn't mean that no one else will.

If you claim that no one will bid $1.00 against your opening bid of $0.99, because they would know that you would stand to lose less by outbidding them and this would in turn neccessitate their outbidding you etc .. then the same logic can be extended to argue that no one will bid $0.99 against your opening bid of $0.98, because they would know that you would have to outbid them etc .., all the way down to no one will outbid an opening bid of $0.01.

The point is this. We can argue, either that everyone is a perfect logician, hence no one outbids anyone, because everyone knows that a second bid invariably starts a bidding war, or that there are a few imperfect logicians in the crowd, hence a second bid will be made against any opening bid below $1.00. We cannot argue that a crowd of some perfect and some imperfect logicians, somehow transforms itself into a crowd of all perfect logicians as soon as the 'magical' opening bid of $0.99 is made.

The problem states that 'everyone will want to do what is best for them'. But, wanting to do something does not always make one capable of doing it. So, while everyone can reasonably calculate their immediate gains or losses from their bidding or passing, there will be at least some who will fail to figure out the long term impact of their bidding or passing, in terms of its likelihood of starting or preventing a bidding war.

The 'winning' strategy must therefore render any further bidding disadvantageous, 'in the moment'. This can only be guaranteed by an opening bid of $1.00.

Posted by Sanjay on 2003-06-10 10:42:59