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Handbook > Auctions > Useful concepts in Auction Theory > Winner's Curse Printer Friendly

Winner's Curse

A key feature of bidding in auctions with common-values components is the "winner's curse": although bidders may obtain unbiased estimates of the item's value, they usually only win in cases where they have the highest of all of the value estimates. Unless this statistical property is accounted for in the bidding, it can result in winning bids that produce below normal or even negative profits.

When one buys a house, a business firm, a work of art or many other kinds of property, it is ususally the case that other potential buyers have decided against purchase (at the posted asking price) or submitted a lower bid than one's own bid (in an auction). This suggests the following questions to a reflective buyer: "Were they right or am I right? Did I perhaps pay more for the property than it is worth?" The possible answers depend on your reasons for buying the property.

If your only reason for buying the property was to enjoy owning it, and you had no intention of ever reselling it to anyone else, and you were sure about the monetary equivalent V to you of consuming the property, then you can be sure that you did not pay more for the property than it is worth so long as you paid less than V. The reason the answer is so clear in this case is that the above assumptions(in the long "if" statement) imply that the only relevant value is your consumption value V that is known to you.This is the case of independent private values that we discuss elsewhere

Now suppose that your only reason for buying the property was for investment purposes, so that your only concern is the future marker value of the property. In that case, you may have good reason for concern if you were willing to pay more for a property than several (or numerous) other buyers. The explanation goes as follows. Suppose that you were competing against some number N>= 1 of other potential buyers for the property. Suppose that no one knows how much the property is actually worth For example, the property may be a business firm with presently unknown future profits or an oil lease to a tract that may or may not turn out to contain oil. Suppose that each of the potential buyers has an estimate of the value of the property that he uses in deciding the maximum amount to pay for it. Typically, some of the estimates will be lower than the actual value of the property and some will be higher. But in a competitive environment such as an auction or contest to buy ("take over") a company, the buyer will usually be one with a higher,or the highest, estimate of value. And, the highest out of N estimates of the value of the property is likely to be higher than the actual value. Therefore, in order to avoid a significant risk of paying more (in a competitive environment) for a property than it is worth, the potential buyer with the highest estimate of value must discount his high estimate in deciding the maximum amount to pay or bid? You cannot know before the competition whether uour estimate is high or low. Thus to avoid the winner's curse you must assume that any estimate you may have is the highest estimate ...and discount the estimate in deciding your maximum willingness to pay or bid ...because you are only likely to outbid all of your rivals if your estimate is in fact the highest one.

Mathematical analysis of the relationship between value estimates and the winner's curse is based in the properties of order statistcs. It was first developed in the context of bidding on oil leases by Capen, Clapp, and Campbell (1971). Analysis of the winner's curse and order statistics when the bidder has multiple estimates of value was developed by Cox and Hayne (2002)

References

Capen, E., R. Clapp, and W.Campbell (1971). "Competitive Bidding in High Risk Situations," Journal of Petroleum Technology 23, 641-653 Cox, J.and S.Hayne (2002)."Barking up the Right Tree: Are small Groups Rational Agents?", Working Paper, Department of Economics, University of Arizona.

 
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