
Uncertainty and Imperfect Information in Markets
337
Define
as the value of s that solves
It is readily shown that the assumptions given imply that
exists and is unique. The
Spence-Mirrlees condition and (6.4.35) ensure that
hence, a high-type seller would prefer to send signal
than to shutdown or be seen as
a low-quality seller. It is readily seen that the one-shot game satisfies the conditions of
Proposition 6.17. Consequently, the only reasonable PBE of the one-shot game is the
least-cost separating equilibrium in which a low-quality seller either does not sell (if
<
c
) or sells without signaling (if
c
), while a high-quality seller ...