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(4): Dollars and Sense by Sanjay)
Okay, so where we differ is in how far a bidder can see/guess the future.
I understand your logic, and I'm sure you understand mine. I can't argue against the first bid of $1.00 being a solution. I don't think it's a very good one, however, as it risks exactly what it returns (nevermind that, the problem forces a first bid). I take "what's best for them" to mean a player will not unnecessarily risk money (why risk what you already have?).
There is one -earthly- reason (maybe not according to formal logic) to make a bid of $2 against $1. If I bid 99c following my strategy and someone figures he can spite me and break even by bidding $1, then I bid $2 (losing 99c and $1 is about the same to me). I do this to demonstrate to all bidders the risk of bidding $1 against 99c. In successive auctions, very few people would consider bidding $1 against 99c. As long as there are a lot of auctions, I can win back my loss and more. Yes, it's a stretch considering the scope of the problem, but I can't come up with a counter stategy to beat it.
Anyway, we must agree to disagree, as any solution relies on psychology after all. Have you considered what happens if the auction is blind (a maximum of one bid per bidder, written on a scrap of paper and handed to the auctioneer)?
re(5): Dollars and Sense
