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.[1]

Play

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 a 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 or she bid without getting anything back. The game begins with one of the players bidding five cents (the minimum), hoping to make a ninety-five-cent profit. He can be outbid by another player bidding ten cents, as a ninety-cent profit is still desirable. Similarly, another bidder may bid fifteen cents, making an eighty-five-cent profit. Meanwhile, the second bidder may attempt to convert his loss of ten cents into a gain of eighty cents by bidding twenty 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.[1]

This game can be "beaten" in a sense if all players are superrational. In this case, any of the n players will bid five 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 five cents. Once that player has locked in his five-cent bid, the other players could bet ten cents, but they would not because they recognize the inevitable standoff as a result of their superrationality. Hence, the auctioneer loses ninety-five 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 ninety-five cents, for a five-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.

Notes

1. ^ a b Shubik: 1971. Page 109