Volunteering and the Strategic Value of Ignorance



which again is equal to V (1 pL) exp (1/2 + T/c) c. Hence, i is indifferent to all
t E (0, c/2 + T] U {T}. Any ti E (c/2 + T, T) leads to a lower payoff.

Now turn to j and suppose that i follows Fi. The equilibrium strategy of jH
follows from Lemma 1. For jL, a concession in t E [0, c/2 + T] yields an expected
payoff of

I (v x) —e cl dx + e cl (v cL t)

= V Cl-


Jo         cl

Hence, jL is indeed indifferent to all t E [0, c/2 + T]. For all t > c/2 + t, jLs
expected payoff is strictly lower. The ex ante expected payoffs in the second row of
(6) and (7) follow directly from these calculations.

A.4 Proof of Lemma 4

By Assumption 1 and Lemma 1, FiH (t) = 0 for all t < T and FiH (t) = 1 otherwise,
i = 1, 2. Thus, for iL, a concession in T is strictly preferred to any t E (cL/2 + T, T).
Suppose that
jL follows FjL. For any ti E [0,t), iL’s payoff is

Pl / (vx)

Jo


----e cl dx + e cl
PlCl


(vti cL ) = vcL-


By choosing ti = T, iL gets

Pl


[t (vx)

Jo


PlCl


cl dx +


cL (v


CL)


Cl + exp

+CL)∙


If

^2~ + TCL ln(1 pL) ,                                               (13)

c = — ɪ + T, and iL is indifferent between all ti E [0,t) U {T}: (13) implies that
FiL (t) < 1 and iL waits until T with strictly positive probability. If (13) is violated,

30



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