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: Here's an idea by Brian Smith)
Hey, fellow Smith!
After a few hair-raising auctions (assuming we can play more than once), all players should realize:
A higher bid means both less profit and more loss (depending on the outcome of the bidding),
A lower bid means both more profit and less loss (again, depending on the outcome),
and,
that the outcome is effectively random.
I can't prove this, but unless you can get into the minds of the other players, you really have no way of influencing the outcome of the auction. For example, consider the type of auction where the bidders write a single bid on a piece of paper. That guy could be bidding low, and the other guy could be bidding high. Who knows? Even in a open auction, where bidders yell out their bids and bidding wars occur, how can we know when the other guy will stop?
So, I think that the tendancy will be for lower bids in the long run.
Also, people were talking about bidding a dollar and breaking even just to spite the other guy. Seriously, if the other guy faces losing 90 cents, why wouldn't he bid $1.10 to win the auction and reduce his loss to 10 cents. Actually, any bidding war supports the argument that the outcome is random. He bids $1.10 and now you face losing $1.00, so you bid $1.20 (cut your loss to 20 cents). This goes up and up until the difference between winning and losing is negelgible. Finally, you pay $8000 for $1, and he's out $7999 for losing. Where does the bidding eventually stop? Who knows? Random outcome.
re(2): Here's an idea
