Category: Effects
Type: Judgment bias in a common-value auction
Origin: E. C. Capen, R. V. Clapp, and W. M. Campbell, Journal of Petroleum Technology (1971); the jar auctions in Max H. Bazerman and William F. Samuelson, Journal of Conflict Resolution (1983)
Also known as: Adverse selection against the high estimate
Type: Judgment bias in a common-value auction
Origin: E. C. Capen, R. V. Clapp, and W. M. Campbell, Journal of Petroleum Technology (1971); the jar auctions in Max H. Bazerman and William F. Samuelson, Journal of Conflict Resolution (1983)
Also known as: Adverse selection against the high estimate
Quick Answer — Winner’s Curse is the shortfall on a winning bid when the object has one value for every bidder and the bid that wins is the one whose estimate was high. Capen, Clapp, and Campbell named the pattern in 1971 from sealed bids on offshore leases. In the 1983 classroom, value estimates averaged 10.01, against objects worth $8.
What is Winner’s Curse?
Winner’s Curse is the shortfall that shows up when a winning bid, in an auction where the object is worth the same amount to every bidder, was built from an estimate that won because it was the high one. A common value is a worth the bidders share. The oil in one tract has one size. The coins in one jar have one total. The resale price of one used car is one market price, even when each mechanic’s note disagrees. The highest note is the note most likely to sit above that shared worth. A bid that treats the note as an ordinary draw, and then wins, is the bid most exposed to the gap. Picture four friends pricing the same car for resale. The friend who trusts the highest note is the friend most likely to pay above the market.If one wins a tract against two or three others he may feel fine about his good fortune. But how should he feel if he won against 50 others? Ill.That line is from E. C. Capen, R. V. Clapp, and W. M. Campbell, page 645, as Richard H. Thaler quotes it in the Journal of Economic Perspectives in 1988. Winning against more rivals is news that the estimate sat further out in the high tail. Overconfidence Effect is a claim about one’s own score, one’s rank against one other person, or the width of a range. Winner’s Curse is the selection an auction performs when it keeps the high estimate and drops the rest.
Winner’s Curse in 3 Depths
- Beginner: The highest guess of the cash in a jar is the guess most likely to be too high. Treat “I won” as news about your guess.
- Practitioner: Before the bid goes in, rewrite the value as the value given that your estimate is the highest, and write the number of rivals on the same line. In the 1983 classes the bids did not fall as that announced count rose.
- Advanced: A rational bid already contains a shade for the fact of winning. Kenneth Hendricks, Joris Pinkse, and Robert H. Porter, in the Review of Economic Studies in 2003, reject a model in which wildcat bidders ignore that fact. The shortfall shows up when the shade is too small. A private value, or a profit figured on a different oil-price path, is a different sentence.
Origin
Winner’s Curse enters the literature in June 1971, in “Competitive Bidding in High-Risk Situations,” Journal of Petroleum Technology, volume 23, pages 641–653. The authors are E. C. Capen, R. V. Clapp, and W. M. Campbell of Atlantic Richfield. They write about sealed bonus bids for oil and gas leases. Their premise, in the abstract, is that the lease winner tends to be the bidder who most overestimates reserves, so the bidder who looks successful may have overpaid. On page 641, as Thaler quotes them, they say that if one sets aside the years before 1950, when the land was cheaper, the Gulf of Mexico “paid off at something less than the local credit union.” They do not print one industry rate of return in that passage. Thaler, on page 197, reports the bid dispersion they describe. Among what they call serious competitors, the ratio of the highest bid to the lowest is commonly as high as 5 to 10, and it can reach 100. In the 1969 Alaska North Slope sale, the winning bids sum to 370 million. The winning bid is at least twice the second bid on 77 percent of the tracts, and at least four times the second bid on 26 percent of the tracts. Thaler writes that these figures do not prove the bids were irrational. Fifteen tracts in the sample they analyzed carried a low bid entered in the hope that no one else would bid.He who bids on a parcel what he thinks it is worth, will, in the long run, be taken for a cleaning.Thaler gives that line as theirs. The remedy they point at is a bid below the estimate, larger in the shade when more rivals are in the sale. The later lease record is Hendricks, Porter, and Bryan Boudreau, Journal of Industrial Economics, volume 35, pages 517–542 (June 1987). They study federal first-price sealed bids off Louisiana and Texas from 1954 through 1969: 8 wildcat sales and 8 drainage sales, 1,056 wildcat tracts and 144 drainage tracts. Those counts leave out 81 wildcat tracts and 25 drainage tracts on which the high bid was rejected. Sales off Florida and the Pacific coast are dropped. A wildcat tract is in ground that is still new. A drainage tract sits next to a tract where a deposit has already been found. Real revenue and drilling cost are discounted at 5 percent a year. Real wellhead prices are held at the sale-year price, so the oil-price jump after 1973 is not in the profit. The royalty in the sample is one-sixth of revenue. Ex post net profit is five-sixths of revenue, minus drilling cost, minus the winning bonus. The figures are before tax. Presale surveys and bid-preparation costs are left out. If a tract was still producing in 1980, output after the peak is projected to fall 25 percent a year for 15 years, and then to stop. In millions of 1972 dollars, the wildcat means are a winning bid of 2.67 (standard error of the mean 0.18), net profit of 1.22 (0.50), and tract value of 5.27 (0.64), with 3.46 bidders. Of 1,056 wildcat tracts, 748 were drilled and 385 were productive. The drainage means are a winning bid of 5.76 (1.07), net profit of 4.63 (1.59), and tract value of 13.51 (2.84), with 2.73 bidders. Of 144 drainage tracts, 124 were drilled and 86 were productive. Hendricks and Porter, American Economic Review, volume 78, pages 865–883 (1988), say profit was about four times higher on drainage tracts, and that the per-acre gap was larger because drainage tracts were typically half as large. The government took 77 percent of wildcat tract value and 66 percent of drainage tract value, with value defined as the present value of revenues minus drilling costs, and the government’s take as royalty plus bonus. On drainage leases from 1959 to 1969, the same 1988 paper finds that neighbor firms are better informed than non-neighbors. At least one non-neighbor bid in 69 percent of the auctions. Non-neighbor bids were more than twice as numerous as neighbor bids, and neighbor firms won well over half of the drainage tracts on which they bid. Their average share of drainage-tract value is about 44 percent. Non-neighbor net profit is about zero overall: significantly negative where no neighbor bid, and positive where a neighbor did bid. About two-thirds of the drainage tracts had more than one neighbor firm. On 74 tracts with several neighbor firms, only 17 drew bids from more than one of them. John H. Kagel and Dan Levin, American Economic Review, volume 76, pages 894–920 (December 1986), ran first-price common-value auctions in the laboratory. Their abstract reports that auctions with 6 or 7 bidders produced more aggressive bidding than auctions with 3 or 4, and that the larger auctions earned negative profits.
Key Points
The bid has to answer a conditional question. The estimate is a draw. The winning estimate is the high draw. Base Rate Neglect leaves a stated frequency out of a probability. Winner’s Curse leaves the sentence “my bid won” out of the value.1
Read the win as news about the estimate
Capen, Clapp, and Campbell ask how a winner should feel after beating 50 rivals. The answer they give is “Ill.” The shared worth did not rise because more firms wanted it. What rose is the chance that the surviving estimate is the optimistic one. A used-car note that wins a small contest of notes has the same shape. The contest, and the size of the contest, belong in the price.
2
Shade the estimate, then check whether the shade grows
In Bazerman and Samuelson’s 48 auctions, the mean bid moved about 41 cents with each dollar of the mean estimate. Uncertainty and the announced number of bidders did not move that auction-level mean. The estimate and those two factors together explain 58 percent of the variation in the mean bid, and the estimate does almost all of that work. Across 1,676 individual bids, one dollar of a person’s own estimate adds 53 cents to the bid. One extra dollar of width in that person’s 90 percent range takes 3 cents off. The announced group size, again, does not. Anchoring Effect is a later number stuck near a first number. Here the bid stays near the bidder’s own estimate while the rival count changes.
3
Let two effects of a crowd pull in opposite directions
More rivals mean a higher bid is required to win. More rivals also mean a larger shade, because the high estimate is further above the shared worth. In the 1983 classes the average of the constructed winning bids rose with uncertainty and with the announced group size. That regression explains 18 percent of the variation, and the authors warn that a handful of very high bids pull the average around. The average bid itself did not fall as the crowd grew. Kagel and Levin’s abstract puts the laboratory version of the same split on group size: 6 or 7 bidders bid more aggressively than 3 or 4, and the larger auctions earned negative profits.
4
Ask what the seller knows before the bid is accepted
Samuelson and Bazerman, as Thaler sets the problem out in 1988, have a buyer offer for a firm whose value to the current owner is equally likely to be any amount from 100 a share. The buyer would make the firm worth 50 percent more. The owner accepts any offer at or above the owner’s own value, and the owner knows that value. If an offer B is accepted, the owner’s value averages B/2, and the buyer’s value averages three-quarters of B. Three-quarters of B is still below B. Any positive offer that the owner accepts has a negative expected value for the buyer. The arithmetic is the curse in a negotiation where only one side sees the value.
Applications
Use the shade when a bid will be read as a fact about value. Keep each figure inside the sample that produced it.Rewrite the estimate as the winning one
On a lease, a house bought to resell, or a jar of cash, write the value conditional on your note being the highest note. In the 1983 classes the mean estimate was 2.87 under the 10.01. A low average guess did not protect the high guess.
Put the rival count on the bid sheet
The 1983 sheets told each class it was competing in a group of 4, 6, 8, and so on up to 26. The bids did not fall as that number rose. The constructed winning bid did rise. If the sheet has a blank for the estimate and no blank for the number of rivals, the shade has nowhere to go.
Condition on the seller's acceptance
When the seller knows the value and will walk away from a low offer, the offers that succeed are the offers on the worse draws. In the problem Thaler reprints, the buyer’s expected value given acceptance is three-quarters of the offer. A family buying out a shared house, where one sibling has the inspection and the others have a guess, has the same conditional step before anyone calls the price a bargain.
Turn the shade around for a low-bid contract
In a procurement the low bid wins, so the surviving bid is the one that put the cost too low. Planning Fallacy is one plan’s own time and cost. Winner’s Curse is the selection among rival plans. Ask what cost would still win if the bid is the optimistic one, and raise the pad as the number of bidders grows. Capen, Clapp, and Campbell’s discomfort at beating 50 rivals is the same discomfort with the sign reversed.
Case Study
The counted demonstration is Bazerman and Samuelson’s classroom auction, published in December 1983. Four hundred nineteen M.B.A. students in 12 microeconomics classes at Boston University each faced four sealed-bid auctions. The design table lists class sizes from 24 to 54, and those twelve sizes sum to 419. The prose of the paper says the classes varied from 34 to 54. The table is the count this page uses. Unknown to the students, every object was worth 8, so the net payment is 2 prize went to the closest estimate in each auction. No feedback arrived until every auction in the session was done. Each student was told a group size, one of the even numbers from 4 to 26, and was told to compete only with that many people. Everyone in a class received the same size for a given auction. The authors did not split the rooms into those groups. For each announced size they averaged the highest bid across every group of that size that could be drawn from the class. Call that average the constructed winning bid. Across the 48 auctions, the mean of those constructed winning bids is 5.48. That is 8 value. Twelve auctions have a constructed winning bid under 7 and 8 and 9. Across the four objects, the mean estimate is 2.87 below 5.13, the average gap from the constructed winning bid would have been $4.88. The lesson is the selection. A room of M.B.A. students can put the average guess below the cash in the jar and still produce a constructed winning bid above that cash, because the auction keeps the high bid. The 5.48 is the spread of those 48 averages. A handful of very high bids moves them. The $2 prize rewards the estimate, the classes are one university’s M.B.A. microeconomics courses, and nothing in the session is an offshore lease.Boundaries and Failure Modes
Winner’s Curse is the wrong name when the value is private, when a lease profit is carried out of the accounting that produced it, and when a rational shade is described as a loss. The first boundary is the private value. A painting you want on your wall, or a house you want to live in, can be worth more to you than to the next bidder. Paying up to that personal worth is a choice about your own use. The curse on this page needs a worth the bidders share, plus estimates that scatter, plus a bid that ignores the news in winning. Sunk Cost Fallacy is the choice to continue after the money is already spent. The selection here happens at the bid. Optimism Bias is a belief about one’s own future set against a base rate of outcomes. The news here is that the auction kept the high estimate. The second boundary is the accounting. Thaler quotes Walter J. Mead, Asbjorn Moseidjord, and Philip E. Sorensen, The Energy Journal, 1983, page 42. On 1,223 Gulf of Mexico leases issued from 1954 to 1969, they report an average present-value loss of 1.22 million in 1972 dollars, with a standard error of the mean of 0.50, on 1,056 tracts. The two sentences are two accountings of offshore leases. This page does not collapse them into one industry rate of return. The third boundary is the shade a bidder can already have learned. In the 1987 wildcat sales, ex post profit net of the bid falls as the number of bidders rises, and it is negative when that number is seven or more. The authors give two readings and do not choose. One is that bidders failed to cut the bid as the crowd grew. The other is that bidders did not know how many rivals would show up, so a bid tuned to the average crowd is too low when the crowd is thin and too high when the crowd is thick. They say a parametric bidding model would be required to separate the two. Hendricks, Pinkse, and Porter (2003) study wildcat leases from 1954 to 1970 and write that bidders are aware of Winner’s Curse and that their bidding is largely consistent with equilibrium. A model in which firms ignore the information in winning is rejected. The equilibrium test is not rejected on the more competitive set, 752 tracts. On the less competitive set, 501 tracts, they find overbidding that comes from firms overestimating tract values. Participation in a given sale is typically under 25 percent for any one firm. Those 752 and 501 tracts are a later sample, split by a measure of potential competition. They are not a partition of the 1,056 tracts from 1987. Kagel and Levin also note, in a survey of this literature, that some theorists use the name Winner’s Curse for the gap between the naive estimate and the value conditional on winning, including the case in which bidders have already subtracted the gap. This page uses the name for the failure to subtract it. Their phrase for that failure is: you win, you lose money, and you curse.Common Misconceptions
Three stories travel with the lease and the jar. Every win is treated as an overpayment. The classroom average is treated as cash that left a wallet. Any high price is given this name.Whoever wins has overpaid
Whoever wins has overpaid
A bid that already treats the estimate as the high draw can win and still leave a profit. Thaler distinguishes a bid above the value from a profit that is merely below what the uncorrected estimate promised. Hendricks, Pinkse, and Porter reject the model in which wildcat bidders ignore the news in winning. On their more competitive set of 752 tracts, the equilibrium test is not rejected. The name on this page is the missing shade. The win itself is the clue that makes the shade necessary.
The students lost $10.01, or lost $2.01 in cash
The students lost $10.01, or lost $2.01 in cash
The 5.48. The 2.87 under the 2.01 is the gap between 8. The rooms were not split into the groups named on the instruction sheet. No feedback was given between auctions. The $2 prize paid for a close estimate.
A high price, a dry lease, or one firm's loss is this effect
A high price, a dry lease, or one firm's loss is this effect
Neighbor firms’ share of drainage-tract value is about 44 percent in the 1988 study, and non-neighbor profit is about zero only as an overall average. It is negative where no neighbor bid and positive where a neighbor bid. In the 1987 counterfactual, winning every tract a firm bid on, at the bid it submitted, returns more than 2.26 million. Texaco is the exception, at a loss of 1.22 million wildcat mean.
Related Concepts
Winner’s Curse sits next to a claim about one’s own accuracy, a number stuck to a first number, a plan’s own cost, a missed frequency, a cost already spent, and a rosy future. Each neighbor keeps the numbers from its own page.Overconfidence Effect
A score, a rank against one other person, and a range. The auction on this page selects the high estimate out of several. The quiz on that page scores one person’s claim.
Anchoring Effect
A later number pulled toward a first number. In the 1983 bid sheets the bid stays close to the bidder’s own estimate while the announced crowd changes.
Planning Fallacy
One plan’s time and cost, set against how similar plans turned out. A low-bid contract adds a second filter: the auction keeps the plan with the lowest cost.
Base Rate Neglect
A stated frequency left out of a probability. The frequency here is the news that the winning estimate is the high one.
Sunk Cost Fallacy
Continuing because the money is already spent. Winner’s Curse is the selection at the moment of the bid, before that money is spent.
Optimism Bias
A belief that one’s own future beats the base rate of outcomes. An estimate can be unbiased on average and still be too high in the auction that keeps only the top one.