In 1971 three employees of the petroleum giant ARCO (Edward Capen, Robert Clapp, and William Campbell) noticed something odd. Oil companies bidding for offshore drilling rights in the U.S. government’s first-price auctions seemed to be suffering unexpectedly low rates of return on their investments, often finding much less oil underground than they had hoped. Why did the oil companies—which on average are pretty good at guessing how much oil lies buried in a tract—seem so often to pay more than the tract turned out to be worth?
As an analogy, imagine that a jar of nickels is being sold in a sealed first-price auction. The jar holds $10 in nickels, but none of the bidders know that; all they can see is how big the jar is. The players independently estimate how much the jar is worth. Maybe Alice guesses right, while Bob and Charlie guess the jar holds $8 and $12, respectively. Diane and Ethel are farther off, putting the value at $6 and $14, respectively.
If all the bidders bid what they think the jar is worth, Ethel will win, but she’ll pay $14 for $10 in nickels—what economists call the “winner’s curse.” Even if the jar is sold in a second-price auction, she will still overpay. Although on average the bidders are correct about how much money is in the jar, the winner is far from correct; she is the one who has overestimated the value the most. In 1983 economists Max Bazerman and William Samuelson, then at Boston University, performed an experiment in which M.B.A. students bid on a nickel jar in a first-price auction; on average the winner paid 25 percent more than the jar was actually worth.
To protect themselves from the winner’s curse bidders must follow an odd logic. In any auction presumably some people will overestimate the value of the item. If everyone bids what they think the item is worth, the person with the highest overestimate will win and pay too much for the item. So the safe strategy for each bidder is to assume she has overestimated, and lower her bid somewhat. If she really has overestimated, this strategy will bring her bid more in line with the actual value of the item. If she has not really overestimated, lowering her bid may hurt her chances of winning the auction; but it’s worth taking this risk to avoid the winner’s curse. This reasoning applies not just to bidders for jars of nickels but also to oil companies bidding for drilling rights, baseball managers bidding for players’ contracts, dealers bidding for paintings, and bidders in any situation where the item has some intrinsic value about which the bidders are uncertain— what economists call “common value” settings.
In the late 1960s economist Robert Wilson of Stanford University decided that game theory was the way to understand common value auctions, and he convinced many of his students and colleagues to think the same. Wilson used the Nash equilibrium to figure out just how much bidders should subtract from their value estimate to provide a good safety net against the winner’s curse. Again, the optimal strategy depends partly on the number of bidders. But in this case the more bidders in the auction, the more each bidder should lower her bid, because if there are many bidders, the distribution of their value estimates is probably very spread out, with the most optimistic bidder greatly overestimating the value of the item.
In common value settings the four standard auctions are not all created equal. In 1982 auction theorists Paul Milgrom (a former student of Wilson) of Stanford University and Robert Weber of Northwestern University showed that an open English auction usually raises the most revenue—the reason roughly being that because each bidder can see how high the others are going, she will be less afraid she has overestimated and will bid more aggressively.
