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 TomM)
This is all fine, however, can we expect the other bidders to be so thoughtful? Although I agree with your logic, I think that there is a bid that guarantees a win and takes into account human nature.
Bid first, bid 99 cents, because...
bidders naturally want to change positions as follows:
neutral --> win
win --> bigger win (impossible in this scenario)
loss --> neutral
big loss --> small loss.
So, IF YOU GET TO BID FIRST, bidding 99 cents makes all other possible bids neutral --> loss. Sure, someone could bid $1.00 in what appears to be neutral --> neutral, but they'd be risking at least $1.00 for zero chance of profit, so this is really neutral --> loss.
If you don't get to bid first, don't bid. Don't force the previous bidder to reduce his loss as this will lead to a bidding war.
Any bid less than 99 cents runs the risk of some wiseguy changing from a neutral/loss --> win. While it would be nice to get the dollar for less than 99 cents, bidding less than 99 cents cannot guarantee that you will be the winner.
Any bid over $1.00 is insane, it guarantees a loss (and probably a big one as many others have pointed out).
Finally, not bidding is not a winning strategy.
Appologies for my silly notation, poor spleeing, and use of CAPS.
re: Solution
