Setup
The setup involves an auctioneer who volunteers to auction off a dollar bill with the following rule: the dollar goes to the highest bidder, who pays the amount he bids. The second-highest bidder also must pay the highest amount that he bid, but gets nothing in return. Suppose that the game begins with one of the players bidding 1 cent, hoping to make a 99 cent profit. He will quickly be outbid by another player bidding 2 cents, as a 98 cent profit is still desirable. Similarly, another bidder may bid 3 cents, making a 97 cent profit. Alternatively, the first bidder may attempt to convert his loss of 1 cent into a gain of 96 cents by bidding 4 cents. Supposing that the other player had bid 98 cents, he now has the choice of losing the 98 cents or bidding a dollar even, which would make his profit zero. After that, the original player has a choice of either losing 99 cents or bidding $1.01, and only losing one cent. After this point the two players continue to bid the value up well beyond the dollar, and neither stands to profit.
Read more about this topic: Dollar Auction