Dollar auction

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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.

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 their loss of 1 cent into a gain of 96 cents by bidding 4 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.

See also

• All-pay auction
• Behavioral finance
• War of attrition (game)

Further reading

• 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.