The Winner’s Curse

The winner-loser

In his paper Anomalies: The Winner’s Curse, economist Richard Thaler proposes a way for us to take money from our friends. First, we find a large jar and fill it with pennies. Next, we bring the jar to our friends, classmates, or colleagues for an auction, and tell them that the highest bidder will win cash in equal value to the sum worth of pennies in the jar.

How much do you think your friends will bid?

Studies on the wisdom of crowds tell us that groups of people are surprisingly good at guessing quantities. Although economic theory tells us that the average bid may be a bit below the value of the jar due to risk aversion. However, there is uncertainty about the jar’s true worth. And by definition, the winning bidder is the one who bids most greatly. So if you have enough friends or classmates, there is a good chance that someone will overestimate its value, netting you a tidy profit.

In fact, Max Bazerman and William Samuelson ran this experiment with MBA students at Boston University and observed similar results. They asked their students to participate in a sealed-bid auction for jars of pennies and nickels worth $8.00. Of course, the true value was unknown to the students. And while the student’s average estimate of the jar was $5.13, the average winning bid was $10.01. So the average winner lost $2.01 simply by playing. (But don’t you fret. Each of them graduated to pursue high-paying salaries as decision-makers for large corporations.)

The coin-jar problem is an example of the winner’s curse. The idea was first formalized in the early 1970s by Atlantic Richfield engineers—E.C. Capen, R.V. Clapp, and W.M Campbell. The problem, as it is formalized today, asks us to imagine that many oil companies are bidding for drilling rights in some remote location. Like the coin-jar, this is a common-value auction. That is to say that while the right-to-drill will be worth the same to whoever wins, no company will know its exact value until drilling begins.

It might be reasonable to assume that companies estimate values correctly on average. But in any one auction, companies will misestimate. In turn, the company that wins the auction must be the one who overestimates and overbids the most.

What’s precarious about the situation is that everyone believes themselves to be acting reasonably. Yet the auction acts as a selection device for bidders who are wrong in the most unfavourable way. As Thaler explains, the winner’s curse can manifest in two ways: “(1) the winning bid exceeds the value of the tract, so the firm loses money; or (2) the value of the tract is less than the expert’s estimate so the winning firm is disappointed.”

“He who bids on a parcel what he thinks it is worth will, in the long run, be taken for a cleaning… Even though each bidder estimates his value properly on average, he tends to win at the worst times… The error is not the fault of the explorationists… The problem is simply a quirk of the competitive bidding environment.”
E.C. Capen, R.V. Clapp, & W.M. Campbell. (1971). Competitive Bidding in High-Risk Situations.

Losers everywhere

The winner’s curse is not isolated to MBA students or oil magnates. As Thaler notes, they can happen to book publishers that wrestle for new authors, to baseball teams that vie for free agents, to consultancies that compete for contracts, and to corporations that play for acquisitions. The case of corporate takeover is especially curious because the expected returns to the acquirer have long been shown to be muted. Perhaps it is a potent mix of ego, hubris, unrest, lock-in, and the winner’s curse that lead to routine overbidding in the marketplace.

Conventional economics typically assume that agents have clear preferences and make rational decisions. So the curse is an economic anomaly in the sense that the winner is also a loser. As Thaler points out, “acting rationally in a common value auction can be difficult.” After all, it requires the bidder to distinguish “between the expected value of the object for sale, conditioned only on the prior information available, and the expected value conditioned on winning the auction.” Indeed, “solving for the optimal bid is not trivial.”

Coin jar revisited

To see this, let us consider a variant of the coin-jar problem. [1] Let us say, for example, that a traveling salesman wants to sell you a jar of ancient coins. You happen to be a coin aficionado yourself, and hope to add the set to your collection. Unfortunately, while the seller knows its exact value, you do not. And you are not allowed to appraise the collection until the deal is done. Your experience tells you, however, that the collection’s value to the salesman must lie somewhere between zero and $10,000 dollars. Let us also assume for simplicity that the likelihood of value is evenly distributed between this range. With that said, you also happen to be a skilled craftsperson. And whatever the original value of the collection, you will be able to restore the set and raise its worth by 50 percent. Given these conditions, how much will you bid for these coins? Try it yourself before moving on.

[1] The coin-jar variant I present here is a modification of a corporate takeover problem that Thaler presents in his original paper.

Problems with asymmetry

Many people reason that the expected worth of the collection to the salesman is $5,000. And that after its restoration, it must have an expected worth of $7,500 to them. Hence, people choose to bid somewhere between $5,000 and $7,500 to induce a sale and make a profit. The problem with this answer, as Thaler explains, is that it “fails to [consider] the asymmetric information that is built into the problem.”

Remember, the salesman will only accept your bid (B) if it is greater than the original value to him. Hence, an accepted bid implies that the expected value of the collection is 0.5 x B. While you can increase its worth by 50 percent, this raises its final expected value to you to 0.75 x B. Hence, no matter what non-zero price you offer, you are expected to lose money if he accepts your bid. The result suggests that it is better to avoid the traveling salesman altogether.

Coins, contracts, and cleaning

If we substitute coin-collections for government contracts, corporate takeovers, antique furniture, second-hand wares, and whatnot, we get a whole class of very real problems. Should it be surprising that the winner’s curse has not yet bankrupted every buyer in the economic machine? Behavioral experiments show, for example, that people are slow to spot and respond to the winner’s curse. This is so even if it happens to them repeatedly.

Others argue, however, that these are contrived experiments. In the real world, people develop heuristics to avoid routine danger over the long run. We should remember as well that organizations can undertake due diligence to improve their estimates under uncertainty. Moreover, market transactions, while impersonal, are not always one-shot events. Buyers and sellers have some incentive to preserve their reputation and relationships in anticipation of later opportunities. If the shadow of the future is large enough, it may help to foster information sharing and win-win scenarios.

That being said, “it is important to keep in mind that rationality is an assumption of economics, not a demonstrated fact”, writes Thaler. What’s more, an awareness of economic consequences can only take us so far sometimes. Knowledge of the winner’s curse, for instance, may prompt us to shade our bids. But if others wed themselves to the status quo, then we are less likely to participate and win in any given auction. This may be a ‘good enough’ strategy. But many decision makers, I suspect, will find this unpalatable. They want to play and they want to win. Indeed, as Thaler writes, “the study of optimal strategy for games in which one’s opponents are less than fully rational deserves greater attention.”

Sources and further reading

Surowiecki, James. (2004). The Wisdom of Crowds.
Thaler, Richard. (1988). Anomalies: The Winner’s Curse.
Dyer, Douglas., Kagel, John., & Levin. (1987). The Winner’s Curse in Low Price Auctions.
Capen, E.C., Clapp, V., & Campbell, W.M. (1971). Competitive Bidding in High-Risk Situations.
Bazerman, Max., & Samuelson, William. (1983). I Won the Auction but Don’t Want the Prize.