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 apparently rational choices made throughout the game.
Contents
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 second-highest bidder also loses the amount that 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. A series of rational bids will reach and ultimately surpass one dollar as the bidders seek to minimize their losses. If the first bidder bids ninety five cents, and the second bidder bids one dollar (for no net gain or loss), the first bidder stands to lose ninety five cents unless he bids $1.05, in which case he rationally bids more than the value of the item for sale (the dollar) in order to reduce his losses to only five cents. Bidding continues with the second highest bidder always losing more than the highest bidder and therefore always trying to become the high bidder. Only the auctioneer gets to profit in the end.
Analysis
The seemingly rational decisions during the game are in fact clearly irrational once one realizes that they are nothing more than a greedy algorithm, which is of course not guaranteed to give a globally optimal solution. In this case there is actually a globally optimal solution, which is to not play the game at all unless one is certain that there are no other players.