Volunteering and the Strategic Value of Ignorance

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

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

I (v — x) —e ^cl dx + e ^cl (v — c_L — t)

Jo         cl

Hence, j_L is indeed indifferent to all t E [0, —c/2 + T]. For all t > ^{—c/2 + t, j}L^s
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, F_iH (t) = 0 for all t < T and F_iH (t) = 1 otherwise,
i = 1, 2. Thus, for i_L, a concession in T is strictly preferred to any t E (—c_L/2 + T, T).
Suppose that j_L follows Fj_L. For any t_i E [0,t), i_L’s payoff is

By choosing t_i = T, i_L gets

Cl + exp

If

^— ^2~ ^{+ T} < ^{— C}L lⁿ(^{1 — p}L^{) ,                                               (13)}

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

30

<<   <   28   29   30   31   32   33   34   >   >>