Shubik. It illustrates 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.
Dollar auction is an all pay
auction having two player. The auction is for a dollar bill.
The game begins with one of the players bidding 1 cent, hoping to
make a 99 cent profit. The second player will quickly bid 2cents, as a 98 cent profit is
still desirable. Again,first bidder bids 3 cents,converting his loss of 1 cent into a
gain of 97 cents. In this way, a series of bids is maintained. However, a problem
becomes visible the moment bidding reaches 99 cents. Supposing that the other player had
bid 98 cents, he now has the choice of losing the 98 cents or bidding a dollar even,
which would make his profit zero. After that, the first 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.The game actually has no equilibrium,
as two rational players in this game could theoretically lose all of their money to the
auctioneer. Both players stand to lose money, but the winning bidder loses about 99
cents less than the losing bidder.
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.
