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): Here's an idea by ryan smith)
(continued from last post, I'm such a windbag)
Maybe a good strategy would be to bid randomly (below a dollar of course). Thus, you could not be drawn into suicidal bidding wars and would probably even win a few rounds. Bidding randomly would also mess up other bidders' "strategies". They would be puzzled (Geez, last time he dropped out at 40 cents, but this time he's all the way at 75 cents).
For random bidding with many other players (N),
Average winnings for bids, B, are:
$ = Pwin * B - Plose * B
and with a random outcome, your chances of winning and losing (second place) are the same (1/N):
$ = (1/N)*B - (1/N)*B
It looks like random bidding is a break even strategy, but I think it may be profitable as, on average, I suspect that your winning bids will be higher than your losing bids.
re(3): Here's an idea
