Common value, first-price, sealed bid
The Highest Number in the Room
In this fixed-value Gaussian common-value toy model, symmetric bidders estimate the same hidden worth. Move the crowd size and noise, then watch unbiased estimates produce a biased winning bid and negative profit. Under the disclosed assumptions, the order-statistic shade returns mean winner profit to break-even. The simulation recomputes every result live and keeps the classroom evidence separate from the toy model.
Every bidder below is right on average. That does not make the winner right on average. The auction selects one estimate from the entire room: the highest. Winning is new information about the error in your own estimate.
Lot 08, identical worth to every bidder
The value is hidden from bidders and shown here for audit.
TRUE VALUE V = $8.00
More competitors means a more extreme maximum.
Each estimate is V + independent Gaussian noise.
Added to the model correction. Zero targets break-even.
All estimates, mean
computing
unselected pool
Winning estimate, mean
computing
maximum of N
Bid shown, mean
computing
naive rule
Winner profit, mean
computing
V minus winning bid
Preparing the auction.
The blue figure and the red figure are made from the same draws. Across all bidders, the estimate mean stays near the true value. Among winners, the estimate is pulled upward. Nothing about the noise changed. Only the instruction keep the maximum changed.
naive bid = signal_i
naive E[profit | win] = V - E[max(signal_1,...,signal_N)] < 0
The information inside winning
The correction is not a vague instruction to be cautious. In this disclosed model it is a number. If M_N is the maximum of N standard-normal errors, its expected value is computed from the density of the maximum:
shade = sigma E[M_N] + reserve margin
corrected bid = signal - shade
The conditioning event changes the bid
Before the auction, a signal error has mean zero. Conditional on the event that your estimate is the maximum of N draws, its error has positive mean. The order-statistic shade subtracts that mean maximum-selection bias across repeated auctions. It does not condition on the realised lot value or calculate a posterior value for a particular signal. In this fixed-value toy model, it calibrates mean winner profit to break-even.
Current live correction
computing
More rivals, a lower bid
Ordinary competitive instinct says that more rivals require a more aggressive bid. A common-value auction reverses that instinct. More rivals make the winning estimate more exceptional, so the correction must grow. The table uses the current noise setting and recomputes the integral in your browser.
| Bidders N | E[max Z] | Required shade | Naive expected profit | Corrected expected profit |
|---|
The jars that made the loss visible
Bazerman and Samuelson's 1983 classroom study auctioned containers with a defined value of exactly $8.00 to MBA classes. Across the study's class-auction aggregates, participants underestimated the contents, yet the winners still overpaid.
$5.13
Mean estimate, $2.87 below the true value.
$10.01
Mean winning bid, $4.88 above the mean estimate.
-$2.01
Average winner profit: $8.00 minus $10.01.
Those figures combine many class runs, not one dramatic session. The classroom estimates were biased downward, unlike the simulator's deliberately unbiased signals. That makes the observed overpayment more striking, but it does not calibrate the simulator. The similar default loss is a rough visual correspondence, not a fitted replication.
Capen, Clapp, and Campbell introduced the phrase "winner's curse" in 1971 while discussing competitive bidding for Outer Continental Shelf petroleum leases. They supplied the name and oil-lease setting. Bazerman and Samuelson supplied the later classroom demonstration. Whether oil firms actually failed to adjust enough in field auctions remains disputed, so this page does not use oil-company losses as its proof.
The check
Observed data
The 1983 paper reports a true value of $8.00, mean estimate $5.13, and mean winning bid $10.01. The displayed loss is arithmetic: $8.00 - $10.01 = -$2.01.
Diagnostic inference
computing
This is the selection claim: the maximum estimate exceeds the unselected mean on average. It does not say every winner loses.
Toy-model output
computing
Run the independent check: node research/winners-curse/verify-winners-curse.mjs.
Assumptions, uncertainties, and free choices
Fixed common value. Every round uses the same $8 value. Bidders do not know it, but the audit does. In real common-value auctions the value itself is uncertain, information can be correlated, and bidders learn from more than signal rank.
Signal model. Independent Gaussian errors are a free modelling choice. The bidder slider, noise slider, 30,000-round display, numerical integration bounds, deterministic seed, and first-price sealed-bid rule are also free choices. Different signal distributions change the shade, but any non-degenerate maximum has the same selection direction.
Correction. Subtracting sigma E[M_N] is the break-even correction for this repeated fixed-value model. It is not asserted as the general Bayesian Nash equilibrium strategy. Risk preferences, priors, affiliated signals, reserve prices, entry, and auction format can all change an equilibrium bid.
Monte Carlo uncertainty. Live values vary by seed. The exact model target comes from numerical integration; the simulated mean approaches it with sampling error. The optional reserve margin makes corrected expected profit positive in the toy accounting, but would also reduce the chance of winning in a strategic auction. This page holds the winner selection fixed to isolate the maximum-selection correction.
Historical boundary. The classroom aggregates establish experimental overpayment in that task. They do not show that winners always lose, and they do not settle contested field evidence from oil leases. Rational shading can eliminate the expected loss. The curse names the error made when a bidder ignores what winning says about a noisy signal.