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22 BIAIS AND FAUGERON-CROUZET
Denote D(p) the cumulated demand stemming from limit orders placed at prices
equal to or higher than p. The optimal Mise en Vente arising in our framework is
described in the next proposition:
PROPOSITION 4. If
N−1 N − 1
c < k(1 − π)
N S
¯Q − S
(N − 1) ¯Q + S ′
the optimal mechanism can be implemented with a Mise en Vente where (i) the reservation
price is v0,(ii) investors place limit orders at prices p ∈{v0,v1,...,vN−1,
pN }, (iii) the price schedule is
if D(pN ) < S, then p = v0, while if D(pN ) ≥ S,
then p = max p D(p) [ N ] +, min{p, s.t., D(p) = D(pN
)} ,
(where [.] + means that if the number within brackets is not an integer it is rounded
up to the next integer), (iv) the equilibrium strategies of the investors are to demand
Q shares at price pn for investors with good signals, to demand S shares at price
v0 for investors with bad signals, and to demand S(1 − k) shares at price v0 for
retail investors.
In the optimal Mise en Vente, consistent with the workings of the actual mechanism,
prices increase with total demand, as the latter is equal to
n ¯Q + (N − n + 1 − k)S.
In equilibrium, in the optimal Mise en Vente, investors with good signals place
more aggressive demands, as they are more eager to purchase the shares. Consequently,
the higher the value of the asset, the better the private signals, the higher
the demand, and the higher the IPO price. This theoretical result is consistent with
the empirical findings by Derrien and Womack (1999) that this auction-like IPO
method efficiently incorporates market information into IPO prices.
Yet, the price set in this mechanism does not clear market in order to satisfy
the incentive compatibility constraint. Correspondingly, there is oversubscription
at the IPO price.
Our analysis suggests that the Mise en Vente and the Book Building methods
have similar incentive properties and can reach similar outcomes. This contrasts
with the discussion in Benveniste and Wilhelm (1990) that, with uniform prices
and even-handed allocations, information revelation should be impossible. The
point is that, in the Mise en Vente, while the pro-rata allocation rule is indeed
even-handed, it leads to investors with different signals being treated differently
because they have placed different bids.