The Dollar Auction: Irrational Escalation of Commitment

The dollar auction is a game designed by economist Martin Shubik to illustrate a paradox brought about by traditional rational choice theory in which players with perfect information are compelled to make irrational decisions.

The setup involves an auction for a one 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. The second highest bidder might not have to pay on eBay, but in many real contests, both sides end up paying but only one gets the prize--like lawsuits, sports competitions, gambling and political campaigns.

Bidding when the price is below fifty cents or so seems harmless because it’s an obvious deal to buy a dollar for any amount less. The twist becomes clear about when the high bid is 80 cents. People start to think about how the second rule–the one requiring the loser to pay–would affect incentives. What might the second highest bidder think at this stage? He is offering 70 cents but being outbid. There are two choices he could make:

• do nothing and lose 70 cents if the auction ends
• bid up to 90 cents, and if the auction ends, win the dollar, and profit 10 cents

But this action has an effect on the person bidding 80 cent, who is now the second highest bidder. This person will now make a similar calculation. He can either do nothing and lose 80 cents if the auction ends, or he can raise the bid to a dollar and have a chance of breaking even. Again, bidding higher makes sense. Thinking more generally, it always make sense for the second highest bidder to increase the bid.

Soon people will bid more than one dollar and fight over who will lose less money. It is the incentives that dictate this weird outcome. Consider an example when the highest bid is $1.50. Since the high bid is above the prize of $1, it is clear no new bidder will enter. Hence, the second bidder faces the two choices of doing nothing and losing $1.40, or raising the bid to $1.60 to lose only 60 cents if the auction ends.

In this case, it makes just as much sense to limit loss as it does to seek profit. The second highest bidder will raise the bid. In turn, the other bidder will perform a similar calculation and again raise the top bid. This bidding war can theoretically continue indefinitely. In practical situations, it ends when someone chooses to fold. This game is played at Stanford in economics classes, and its not uncommon to see the game end anywhere between five and ten dollars.

Here are some other real life examples of the irrational escalation of commitment:

• After a heated and aggressive bidding war, Robert Campeau ended up buying Bloomingdale's for an estimated 600 million dollars more than it was worth. The Wall Street Journal noted that "we're not dealing in price anymore but egos." Campeau was forced to declare bankruptcy soon afterwards.
• Supporters of the Iraq War have used the casualties of the conflict in Iraq since 2003 to justify years of further military commitment. This rationale was also used during the sixteen-year Vietnam War, another military example of the logical fallacy.
• Two competing brands often end up spending money on advertising wars without either increasing market share in a significant manner. Though the most commonly cited examples of this are Maxwell House and Folgers in the early 1990s, this has also been seen between Coke and Pepsi, and Kodak and Polaroid.
  
• Shakespeare's Macbeth comments, "I am in blood stepped in so far that, should I wade no more, returning were as tedious as go o'er." The metaphor represents Macbeth's crimes and rather than stop committing crimes (presumably, for fear of damnation) Macbeth says that he has "passed the point of no return" and might as well continue, even though it will inevitably lead to his downfall.