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(2): Dollars and Sense by Sanjay)
Please don't misunderstand my reasoning. Here are my two key points:
-ANY bid puts money at risk.
-Bidders can calcualte their potential gains and losses for a potential bid. I.e. They are capable of thinking: "If I bid X, I may win Y or I may lose Z." Such immediate outcome perception is reasonable for any gambling problem. Consider a silly guess a card problem (52 cards, guess the top card): If I bet $1, I may win $52 or I may lose $1. There is so extraordinary logical foresight required.
So, a second bid of a dollar undoubtedly risks (or commits) $1.00 for zero possible return. There is no logical motivation for this bid. The moment the second bidder utters "I bid $1.00" they are bound to either lose $1.00 or win NOTHING. A bidder understanding this is not a "long term impact", it it part of the reasoning process for any bid!
If the first bid is 98 cents, an imperfect logician in the crowd may reason that if they bid 99 cents they can make 1 cent. So, there is some logical motiviation for a second bid of 99 cents.
Also, you've mentioned that a second bid invariably starts a bidding war. Prove it. Someone bids $2 against $1. Both are down $1. Bidding war?
re(3): Dollars and Sense
