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14 BIAIS AND FAUGERON-CROUZET
risk neutral, and this is a common value auction. The objective of the seller is to
maximize the proceeds from the sale.
Each large investor can buy the whole issue and observes a private signal si, i =
1,...N. The signals are identically and independently distributed and can be good
(g), with probability π, or bad (b) with the complementary probability. The value v
of the shares on the secondary market is increasing in the number of good signals n
and its realization is denoted vn.
The retail investors, as a whole, can purchase up to S(1 − k) shares, with k ∈
[0, 1].
The financial intermediary is assumed to act in the best interest of the seller.
She is in contact with the large institutional investors, and she has a distribution
network, collecting the orders from the retail investors.
Consider the following direct mechanism. Each informed investor i sends a
message mi ∈{g, b}. The mechanism maps these N messages into a price and
into allocations to the informed agents and the retail uninformed agents. The
mechanism is subject to several constraints. First, the price must be the same for
all. This is to reflect the constraint, observed in practice, that IPO auctions involve
uniform pricing (it should be noted, however, that Benveniste and Wilhelm
(1990) show that investment bankers acting in the best interest of the firm could
increase expected proceeds by using price discrimination). Second, since we assume
the N large traders are ex ante identical, the mechanism is symmetric. Hence
the price is simply a function of the total number of investors who report good
signals ˆn, and is correspondingly denoted p(ˆn), while the quantity allocated to informed
agent i depends only on her message mi and the number of other informed
agents who reported good signals, li. Correspondingly it is denoted q(mi; li). Similarly,
the quantity allocated to the uninformed agents depends only on ˆn, and
it is denoted qu(ˆn). Third, the allocation must be such that exactly S shares are
sold.
∀{mi}i=1,....N , ˆn ∈{0,...N},
N
q(mi; li) + qu(ˆn) = S.
The mechanism opens the possibility to allocate different quantities to investors
reporting different signals. Indeed, quantity discrimination is crucial to obtain
information revelation from the investors.
The program of the mechanism designer is to maximize expected proceeds
i=1
Maxqi (.;.),qu(..),p(.)E(Sp(ˆn))
under the incentive compatibility and participation constraints of the investors. The
incentive compatibility constraint of the informed investor i is that she must be better
off announcing her true signal than misreporting it, while rationally anticipating