Online Auctions - Dollar auction

The dollar auction is a non-zero sum sequential game designed by economist Martin Shubik to illustrate a paradox brought about by traditional rational choice theory in which players with perfect information in the game are compelled to make an ultimately irrational decision based completely on a sequence of rational choices made throughout the game.

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 their loss of 1 cent into a gain of 96 cents by bidding 4 cents. In this way, a series of bids is maintained. However, a problem becomes evident as soon as the bidding reaches 99 cents. Supposing that the other player had bid 98 cents, they now have the choice of losing the 98 cents or bidding a dollar even, which would make their 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.

One possible model, by which the dollar auction can be profitable for the bidders and detrimental to the auctioneer, involves two parties bidding cooperatively. The two parties could bid two cents for the dollar together, and each profit 49 cents. However, this ignores the fact that the auction is a public auction. Though the end game only involves two bidders, before the bidding hits 98 cents it is still a “profitable” proposition for any player to enter the bidding. To end the bidding war a bidder can bid 99 cents more than the previous bid, leaving no bid that offers a potentially higher profit (or smaller loss). (For example, Bidder 1 bids $x, Bidder 2 bids $x + $0.99. If Bidder 1 were to bid $x + $0.99 + $0.01, he would be bidding to pay $x + $0.99 + $0.01 for a prize of $1, or a total loss of $x—the same as if he had not increased his previous bid.) As a special case of this, if the first bidder immediately bids $0.99, he will not be outbid by the other bidder, who has no potential to make a profit. The first bidder will earn $0.01 in profit and the second bidder will pay nothing and win nothing. A second refutation involves the fact that any rational person need only play this scenario out to realize it is a losing proposition and not engage in such an auction in the first place. This refutation relies on players being rational, and much psychological and economic evidence suggests that humans are not always rational in this sense.