Ch. 3: Auctions in Corporate Finance 103
- Common-value auctions
3.1. Common value assumptions
To this point we have mostly considered auctions where bidders’ preferences were
described by the independent private values assumptions. Clearly, in this framework,
given their signals, bidders have complete information about the value of the object
to themselves. We turn now to another class of models where each bidder has infor-
mation that, if made public, would affect the remaining bidders’ estimate of the value
of the object. The general model could be described as each bidder having a value
Vi=vi(t 1 ,t 2 ,...,tN), wheretirepresents bidderi’s signal. However, before we turn
to the general model, it is useful to focus on a particularly important special case—the
case of the “pure common value” model. In this scenario, every bidder has the same
valuation for the item, hence the phrase “common value”. In other words, we have
Vi=v(t 1 ,t 2 ,...,tN) (21)for each bidderi. Such an assumption is reasonable for auctions of many assets. The
sale of a company, for instance, is sure to exhibit common-value characteristics, for the
company’s underlying cash flows will be uncertain but, at least to the first consideration,
will be the same for all potential acquirers.^19
Common or interdependent-value auctions involve a certain form of adverse selec-
tion, which if not accounted for by bidders, leads to what has been called the “winner’s
curse”. Auctions are wonderful at selecting as winner the bidder with the highest valua-
tion. However, the highest of several value estimates is itself a biased estimate, and this
fact would cause the winner to adjust downward her estimate of the value of the object.
For example, suppose that there are two bidders, the object is worthv=t 1 +t 2 to each,
where eachtiis an independent draw from the uniform[ 0 , 1 ]distribution. Based on her
signal alone, each bidder’s estimate of the value isti+ 1 /2. However, if the bidders
are symmetric, after learning that she is the winner in a first-price auction, bidderi’s
estimate of the value will change toti+E(tj|tj<ti)=ti+ti/ 2 <ti+ 1 /2.
The point to emphasize here is that under almost any reasonable bidding scenario, the
high bidder will be the one with the highest value estimate. While each bidder’s estimate
is an unbiased ex-ante estimate of the common value, the highest of those estimates is
biased high. Or to put it another way, winning an auction gives a bidder information that
they had the highest estimate of value. If one respects the fact that the other bidders are
as good at estimating value as oneself, then the information thatN−1 other bidders
thought the item is worth less should give one pause for reflection (and of course this
pause should have been taken before the bid was submitted).
(^19) The classroom “wallet game” mimics this particular common value auction model. In this game, two
students are picked and each is asked to privately check the amount of money in his wallet. The teacher then
announces that a prize equal to the combined amount of money in the wallets will be auctioned. The auction
method is a standard ascending auction in which the price is gradually raised until one student drops out. The
winner then gets the prize by paying that price. SeeKlemperer (1998).