For T → cl/2, (14) converges to
—Cl — (ch — cl) + ʒ- (c + cl) — ~PlCl — (ch — c) < 0.
2 2 2
Moreover, deriving (14) with respect to T yields
∂V∕ (T)
∂T
1 Ph / x i-ɪ „
-—(ch — Cl) e2 cl + рн > 0.
2 cl
If cl/2 — cl In pH <T < c/2, using again (4) and (8) we have
Vi (T) — —cl — pH (T + “ù--cl + cl lnpH) + pH (^ + T)
(15)
and
∂Vi1 (T )
∂T
—pH + pH > 0.
(iii) With (4), i gets υ — c if he does not become informed. By the same argument as
in (i) for T > c/2, z’s ex ante payoff in case (I, I) must be strictly larger than υ — c,
and thus Vi1 > 0 for all T ∈ (c/2, ch/2).
(iv) In (ii), monotonicity has been shown for T < c/2. Now suppose that T >
c/2. Consider first the case where T is smaller than cl/2 — cl lnpH, i.e. T ∈
(c/2,cl/2 — cllnpH). (For a sufficiently large pH, this interval is empty.) Then,
with (6) and (8),
p Prr i_τ i τ
Vi1 (T) — —Cl — -^~(ch — Cl) C2 cL + рнce 2 + ð (16)
2
and
∂Vi1 (T )
∂T
Ph , i i--T- _i+τ „
— — (ch — Cl) e2 cl + Phe 2 + ð > 0.
2cl
Now suppose T is larger than cl/2 — cllnpH, but smaller than c/2 — clnpH, i.e.
T ∈ (cl/2 — cl lnpH, min {c/2 — clnpH,ch/2}). (This interval may be empty for a
32
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