Ch. 3: Auctions in Corporate Finance 133
of equilibria with varying degrees of underpricing. The intuition of the underpricing
result is quite simple: in a uniform price auction, bidders are asked to essentially submit
demand schedules, specifying the number of shares they would be willing to buy at
different prices.Wilson (1979)showed that instead of thinking of bidders as selecting
a demand schedule to submit, a simple transformation allows us to model a bidder’s
decision as one of selecting the optimal “stop-out” price after subtracting other bidders’
demands from the available supply. This makes each bidder a monopsonist over the
residual supply and sets up the essential monopsonistic tension: a higher bid increases
the quantity of shares purchased, but raises the price paid on all shares. Optimally, a
bidder will submit a low stop-out bid, and as this will be the case for all bidders, a Nash
equilibrium holds. Interestingly, the literature on underpricing in IPOs has not picked
up on this simple explanation, relying instead on more complicated explanations.
While not relying on the Wilson/Back and Zender insights,Benveniste and Spindt
(1989)nonetheless use an auction-based model to explain certain aspects of the IPO
process. The basic idea is similar to that ofHansen (2001), as it involves conditions un-
der which bidders reveal truthfully their information through bids that are non-binding
“indications of interest”. The model asks under what conditions an investor will reveal
her information to the investment banker collecting demand information for an IPO.
Under-pricing of the IPO guarantees a return to these investors; this is critical for oth-
erwise there could be no incentive to honestly reveal information. Also, those investors
who reveal high valuations must receive more of the under-valued shares, or again there
would be no payoff from honestly revealing information (and there is a cost to honest
revelation as it affects the offering price). Thus, this auction-based model explains two
core features of the IPO process, under-pricing and differential allocations of shares.
Biais and Faugeron-Crouzet (2002)present a complex and quite general model of the
IPO process that compares auctions to fixed-price offerings. Unfortunately, the authors’
conclusion that the book-building approach dominates the auction method is clouded
by the assumption that the auction method will induce collusion between the bidders.
It is not at all clear why collusion, if profitable, will occur only in one auction method.
This paper also shows why it is extremely difficult to use auction theory to convincingly
show that one method is more efficient than another: to do this, one must introduce
a myriad of assumptions, covering everything from valuations to costs of information
collection. The validity of all these assumptions is difficult to evaluate, and the chances
that the ranking of the sales methods would change, or become indeterminate, is high if
some of the assumptions were changed.
Sherman (2005)compares bookbuilding to auctions under the very reasonable as-
sumption that entry by bidders is an endogenous decision. Her model yields a result
similar in spirit to a core result that emerges from comparing the basic auction methods
that while the expected price is the same in sealed-bids versus second-price auctions, the
variance of prices is greater for the second-price auction. This result comes about be-
cause in the first-price auction, bidders put in their bids using theirexpectationof what
other bidders’ values are, while in the second-price auction, the high-bid is dependent
on theactualvalue of the second-highest valuation. Sherman focuses on the uncertainty