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A dollar auction is the name of a non-zero sum sequential game designed to illustrate the phenomena where players end up making irrational decisions based on a rational choice. The game begins when the auctioneer offers to sell $1 US Dollar (USD) at auction with two stipulations: Each bid must be higher than the previous one, and the second-highest bidder must also pay his or her bid. If the winning bid is $0.99 USD and the losing bid is $0.98 USD, both bidders pay their respective bids.
The novelty of the game is that as the bids increase, the focus shifts from achieving the greatest gain to minimizing loss. The dollar auction might start out with bids of $0.01 USD and $0.02 USD, but as the bids near $1 USD, the focus shifts. If the high bid is $1 USD or more, the second-highest bidder might increase the bid to minimize the loss. If that bidder wins, he or she will have $1 USD to help offset the bid. Actual play might have participants bidding $3 USD or more for a single dollar bill.
Designed by Martin Shubik, who described it in a paper in 1971, it was his attempt to determine whether addiction could be introduced into game theory. Game theory is the set of concepts that describe strategic interaction between parties to achieve winning outcomes or gain. It is widely used in the field of microeconomics. A zero sum game is where the gains and losses equal zero, such as when one party gains 10 and the other party loses 10.
The paradox in the dollar auction is that each bidder is calculating to gain the advantage, but the bidders continue to lose more and more as the auction progresses. It is comparable to an all-pay auction, which as the name implies, has all of the bidders paying. Political lobbying is an example of this, where all of the lobbyists are paying the costs, and like the dollar auction, only one will be the clear "winner."
In a larger and more insidious example, the principle behind the dollar auction has been applied to what is referred to as a war of attrition. In a war of attrition, the goal is not to win a battle or decisive victory but to systematically inflict the greatest cost of manpower and resources on the opponent. The parallel is obvious, because the bidder with the largest amount of cash will be able to use up the opponent’s reserves. Both will lose money, but the winner who exceeds the loser's bid by the minimum amount possible will lose nearly a dollar less than the second-highest bidder.