Proof of Proposition6.17: It needs to be shown that (a) this is an equilibrium; (b) it
satisfies the Intuitive Criterion; and (c) in light of the earlier lemmas, no other separating
PBE satisfies the Intuitive Criterion.
With respect to (a): the buyer’s beliefs and strategy are obviously consistent with a PBE.
Consequently, a seller’s expected payment, π, is at most
γ
if
s<s
∗
and at most
¯γ
if
s≥s
∗
.
A low-quality seller will not wish to deviate:
for all s > s
0
and, by (6.4.23),
for all
s≥s
∗
. Nor will a high-quality seller:
for all
s<s
∗
, where the second inequality follows from (6.4.14) (i.e., Spence-Mirrlees) ...
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