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): Dollars and Sense by ryan smith)

The '99c' solution relies on a dynamically shifting logical capability on the part of the potential second bidder.

If he can think only one step ahead, then:

The person making the second bid of $1.00 against an opening bid of 99c will figure that he will 'win' the dollar on auction but will 'neither gain nor lose financially', and not that he is 'bound to either win $1.00 or win NOTHING'.
Since he wants to do what is best for him, he will want to 'win' the auction at no financial cost to himself. Hence he will make the bid.

Likewise, the person making the second bid of 99c against an opening bid of 98c will reason that he will 'win' the dollar on auction and 'will make 1 cent' and not that he 'may make 1 cent'. Hence, he will make the bid.

If he can think several steps ahead, then:

The person making the second bid of $1.00 against an opening bid of 99c will figure that he is 'bound to lose $1.00', and not that he is 'bound to either lose $1.00 or win NOTHING'.
He will not want to back a losing proposition. Hence he will not make the bid.

Likewise, the person making the second bid of 99c against an opening bid of 98c will figure that he is 'bound to lose 99 cents', rather than reason that he 'may make 1 cent'.
Again, he will not want to back a losing proposition. Hence he will not make the bid.

In any event:

For an opening bid of 99c to be a 'winning' strategy and an opening bid of 98c to not, the potential second bidder should be able to think ahead at least two steps when the opening bid is 99c, but only one step when the opening bid is 98c. This cannot be guaranteed.

Hence, an opening bid of 99c is not a reliable winning strategy. On the other hand, an opening bid of $1.00 is more 'idiot proof'.

Posted by Sanjay on 2003-06-12 13:42:18