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 bill goes to the winner; however, the two highest bidders must pay the highest amount they bid. The winner can get a dollar for mere five cents, but only if no one else enters into the bidding war. The second-highest bidder is the biggest loser by paying the top amount he/she bid without getting anything back. The game begins with one of the players bidding 5 cents (the minimum), hoping to make a 95 cent profit. He can be outbid by another player bidding 10 cents, as a 90 cent profit is still desirable. Similarly, another bidder may bid 15 cents, making an 85 cent profit. Meanwhile, the second bidder may attempt to convert his loss of 10 cents into a gain of 80 cents by bidding 20 cents, and so on. Every player has a choice of either paying for nothing or bidding five cents more on the dollar. Any bid beyond the value of a dollar, is a loss for all bidders alike. Only the auctioneer gets to profit in the end.
This game can be "beaten" in a sense if all players are superrational. In this case, any of the n players shall bid for 5 cents if they succeed in some independent probability event with a 1/n chance. If it ends up that no bids are made this way, the person holding the auction would either abort or restart the game. If the game continues, one player (the quickest to bid, possibly) will be the highest bidder with 5 cent. Once that player has locked in his 5 cent bid, the other players could bet 10 cents, but they would not because they recognize the inevitable standoff as a result of their superrationality. Hence, the auctioneer loses 95 cents, and the lucky player wins that much, with no second bidder to take from.
This game can also be "beaten" in a second way, provided that all the bidders are bidding in a rational, but not necessarily superrational fashion. If the first bidder bids 95 cents, for a 5 cent profit, none of the other bidders will follow it up with a bid, because there is nothing to gain. However, this will only work if it is the first bid, as if it is not, the second highest bidder will be pushed towards bidding.
- Shubik: 1971. Page 109
- Shubik, Martin (1971). "The Dollar Auction Game: A Paradox in Noncooperative Behavior and Escalation" (PDF file, direct download 274 KB). Journal of Conflict Resolution 15 (1): 109–111. doi:10.1177/002200277101500111.
- Poundstone, William (1993). "The Dollar Auction". Prisoner's Dilemma: John Von Neumann, Game Theory, and the Puzzle of the Bomb. New York: Oxford University Press. ISBN 0-19-286162-X.