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?
Some of my thoughts on positive expectation strategies.
If there is a positive expectation strategy, then it must apply to all bidders. If auctioneer sees a profit, then the net expectation is negative and if the auctioneer sees a loss, then the net expectation is positive.
This means the only way a positive expectation can be realized is if the average sum of the first and second place bids is less than $1.00.