Measured Games  ·  Paper 13 of 07  ·  Auction theory

The winner's curse

After E. C. Capen, R. V. Clapp and W. M. Campbell (1971); laboratory account by J. H. Kagel and D. Levin (1986)

Abstract

When bidders hold noisy estimates of a common value, the winner is disproportionately the bidder whose estimate was too high. Winning is bad news about the estimate that produced it, and a bidder who does not condition on that fact overpays systematically. The correction required grows with the number of rivals, so more competition calls for lower bids, which is the reverse of the intuition most bidders bring.

Keywordscommon-value auction · adverse selection · bid shading · conditional expectation

1Setup

Setup

Several bidders compete for something whose value is the same for all of them but known to none: an offshore tract with an unknown quantity of oil, a company whose true worth is being estimated, a jar of coins. Each bidder forms an estimate. The estimates are unbiased, which is to say they are as often too low as too high.

The auction then does something the bidders did not ask it to do. It selects, from all those estimates, the highest one. Whoever wins is not a randomly chosen bidder but the bidder whose error happened to be the largest in the upward direction. Winning is therefore evidence that you overestimated, and a bidder who has not built that inference into the bid has already lost money at the moment of victory.

2The model

The model

# common value V, unknown; N bidders each see an unbiased estimate xi = V + εi, ε ~ U(-e, e), E[xi] = V # the naive bid treats the estimate as if it were the value bid = xi → wins when xi is the largest of N # but conditional on winning, the estimate is biased upward E[ εi | xi is the maximum ] = e (N-1)/(N+1) E[ V | xi is the maximum ] = xi - e (N-1)/(N+1) # so the required shading grows with the number of rivals N = 2 → shade e/3 N = 5 → shade 2e/3 N = 20 → shade 19e/21

The comparative static is the counterintuitive part and it is worth stating on its own. More competitors means you should bid less, not more, because the winning estimate is drawn from further out in the tail. Bidders who respond to a crowded auction by bidding harder are moving in exactly the wrong direction.

Figure 1Common-value auctions under two bidding rules

One auction · estimates against the true value, winner marked

Winner's average profit against the number of bidders · both rules

Distribution of the winner's profit under the current rule

Estimates Naive bidding Conditioned on winning Break even

Charts are focusable. With a chart focused, use the left and right arrow keys to read values along the horizontal axis.

Required shading—
Winner's mean profit—
Share of wins losing money—
Winner's mean estimate error—
True value—
Auctions0
Figure 1. Every auction is drawn afresh: a true value, N unbiased estimates, and a winner determined by the highest bid under the current rule. Nothing about the curse is scripted, it falls out of selecting the maximum. The middle panel sweeps the number of bidders under both rules at once, which is where the counterintuitive comparative static shows up: the naive line falls away as competition rises, while the conditioned line stays near zero.
3Results

Results

Capen, Clapp and Campbell (1971) named the effect while working at Atlantic Richfield, and their argument was practical rather than theoretical. Returns on offshore leases had been persistently disappointing across the industry despite competent geology, and the explanation they offered was that the bidding procedure itself selected for optimistic estimates. Their advice was to shade bids, and to shade them more where more competitors were expected.

The formal treatment makes the size of the correction explicit. Because the expected maximum of N draws moves outward with N, so does the required shading, and a bidder using an unbiased estimate without conditioning will lose money on average whenever they win. The loss is not caused by bad estimates. It is caused by good estimates combined with a selection rule that only lets the highest one through.

This is the only model on the site whose central mechanism is inference rather than incentive. Nothing in the payoff structure pushes anyone to overbid; what does the damage is a failure to update on an event that has already occurred.

4Evidence

Evidence

Kagel and Levin (1986) took the effect into the laboratory with a first-price common-value auction and found it clearly. Inexperienced bidders earned negative profits, and the losses were worse in larger groups, which is the comparative static the theory predicts and the opposite of what naive competition intuitions suggest. Experienced subjects reduced but did not eliminate the effect.

Dyer, Kagel and Levin (1989) ran the same design with professional construction contractors, whose working lives consist of competitive bidding on common-value projects. They fell into the curse about as readily as student subjects did in the laboratory setting, which suggests that whatever the professionals had learned was tied to the specific structure of their own industry rather than being a general grasp of the inference.

Hendricks and Porter (1988) supply the field counterpart, using data on federal offshore oil and gas lease auctions. Their analysis of bidding by firms with and without private information on neighbouring tracts is broadly consistent with bidders accounting for the adverse selection, indicating that in a repeated high-stakes setting with expert participants the correction does get made.

5Limitations

Limitations

The tidy shading formula depends on the specific assumptions above: a pure common value, symmetric bidders, unbiased estimates with a known error distribution, and no private-value component. Real auctions mix common and private values, and where the private component dominates there is no curse to avoid.

The laboratory evidence is strong for inexperienced bidders and weaker as a claim about markets. Hendricks and Porter's field results and the persistence of the industries in question both suggest that repeated players adapt. The honest summary is that the curse is a reliable feature of one-shot decisions by people who have not met the problem before, and an open question about seasoned bidders in their own domain.

The simulator implements bidding rules rather than equilibrium bidding. Conditioning on winning removes the bias but is not the risk-neutral Nash equilibrium of a first-price common-value auction, which shades further still. The point being made here is about the inference, not about optimal play.

Related This model shares its mechanism with Bank runs (Paper 11) and Focal points (Paper 17) and Brood parasitism (Paper 18). In each of them, what an agent can infer, rather than what they are paid, decides the outcome.

 References

References

  1. Bazerman, M. H., & Samuelson, W. F. (1983). I won the auction but don't want the prize. Journal of Conflict Resolution, 27(4), 618–634. https://doi.org/10.1177/0022002783027004003
  2. Capen, E. C., Clapp, R. V., & Campbell, W. M. (1971). Competitive bidding in high-risk situations. Journal of Petroleum Technology, 23(6), 641–653. https://doi.org/10.2118/2993-PA
  3. Dyer, D., Kagel, J. H., & Levin, D. (1989). A comparison of naive and experienced bidders in common value offer auctions: A laboratory analysis. The Economic Journal, 99(394), 108–115. https://doi.org/10.2307/2234207
  4. Hendricks, K., & Porter, R. H. (1988). An empirical study of an auction with asymmetric information. The American Economic Review, 78(5), 865–883.
  5. Kagel, J. H., & Levin, D. (1986). The winner's curse and public information in common value auctions. The American Economic Review, 76(5), 894–920.
  6. Thaler, R. H. (1988). Anomalies: The winner's curse. Journal of Economic Perspectives, 2(1), 191–202. https://doi.org/10.1257/jep.2.1.191

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