Volunteering and the Strategic Value of Ignorance



For Tcl/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          „

-—(chCl) 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/2cl lnpH, i.e. T
(c/2,cl/2cllnpH). (For a sufficiently large pH, this interval is empty.) Then,
with (6) and (8),

p                    Prr                i_τ              i τ

Vi1 (T) — Cl-^~(chCl) C2 cL + рнce 2 + ð                           (16)

2

and

∂Vi1 (T )
∂T


Ph ,         i i--T-        _i+τ „

— (chCl) e2 cl + Phe 2 + ð 0.

2cl

Now suppose T is larger than cl/2cllnpH, but smaller than c/2clnpH, i.e.

T (cl/2cl lnpH, min {c/2clnpH,ch/2}). (This interval may be empty for a

32



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