Winner's curse

Winner's curse is one of the reasons why prices determined by auctions deviate from "true values" (I mentioned it recently in the context of eBay's apparent plans to capitalize on their transaction data) - auctions, by their nature, tend to favor those bidders who have most overestimated the value of the item for sale. Even if some of the bidders have accurate (unbiased) estimates, the auction favors (or selects) those bidders who have a (postively-) distorted estimate of the value. The winner, therefore, finds himself having overpaid, relative to the true value of the item - this is the winner's curse.

The magnitude of this effect depends on the number of bidders: the more the bidders, the more likely it is that the winning bid seriously overestimates the value. This is intuitively obvious. It turns out that the effect of the number of bidders can be quantified (under the assumption that the bidders' estimates are derived from an underlying normal (Gaussian) distribution): for example, with 2 bidders, the winning bid overstimates the value by 0.56*SD (SD = standard deviation); with 500 bidders, the overestimation is 3*SD; with 1000 bidders, the overestimation is 3.25*SD, etc. [The dependence on N, the number of bidders, seems to be logarithmic, with the multiplier approximated by Log(N) + 0.25. I'll try to derive the general result this weekend and see if this logarithmic rule is correct.]

This suggests a way to correct for winner's curse effects in the eBay example from yesterday - eBay should release the number of bidders, as well as relevant stats on the individual bids, along with the sale price of the item.

What the foregoing also implies is that bidders should reduce their estimates of value by the corresponding factors, to correct for winner's curse. Of course in sealed-bid auctions, in particular, it may be hard to estimate (and correct for) the number of bidders. The standard deviation can also be hard to estimate, in general.

Shifting gears slightly and looking at the problem of auction design, it turns out that, it is desirable to minimize winner's curse effects. This is somewhat counter-intuitive, but the reason is this: visibly reducing winner's curse risk encourages experienced bidders to be more aggressive in bidding, since the risk of overpaying is reduced. The result is that the policy of reducing winner's risk actually increases the amount paid.

Ways to reduce winner's curse effects:
* Release relevant information about other bidders' bids as well as information vailable to the seller. Availability of better information reduces risk of overestimating value.
* Royalties (tie the buyer's payment to the realized value of the item). "For example, the right to broadcast the summer Olympics held in Seoul ... was auctioned with a royalt payment - the amount paid would depend on the size of the television audience." Again, this reduces winner's curse risk by tying at least a fraction of the payment to the actual value realized by the bidder.

I learnt about the winner's curse effect from Preston McAfee's 'Competitive Solutions', which I read recently.