Volunteering and the Strategic Value of Ignorance



PlV +(1 Pl) (T) which is strictly larger than

pLv + (1 Pl) ((vCl) + ⅛ InpH)

= vCl + Cl (1 Ph + Ph In Ph )

> vCl

where the inequality follows from the fact that 1pH +pH InpH 0 for all pH (0,1).

Thus, if T is sufficiently small, only one individual acquires information. For
T ≥ — (vcl)cl InpH, by continuity of the expected payoff in (20), the same
result holds if
T is sufficiently close to — (vcl) cl InpH. For larger T, equilibrium
information acquisition depends on the parameter values.29

B Supplementary appendix

B.l Details on Example 1

Note first that, for cl = 2 and ch = 10, c/2 clnpH ch/2 for all pH (0,1).
Hence, the mixed strategy equilibrium exists for all
T (c/2, ch/2).

(a) For pH = 0.75, we have cl2cl lnpH = 1 2ln0.75 4 = c/2. Hence, using
(15), the value of information if
T c/2 converges to

cl — pH (jT +2   cl + cl lnрн) + pH 2^2 + T)

= 2 -9- (4 + 5 2 + 2ln0.75) + 0.75 (4 + 4) 0.386 0
16

Moreover, Vi1 is negative for all T < cl/2 cl lnpH = 1 2 ln 0.75. By monotonicity,
there is a unique
T (1 2ln0.75, 4) such that h= 0. Setting (15) equal to zero
yields
rT = 1.94.

29Note that, while both (19) and (20) are decreasing in T, the slope of (19) is steeper. As in
Corollary 1, whenever
p is small, it is more likely that only one individual will acquire information
in equilibrium.

37



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