Volunteering and the Strategic Value of Ignorance

Otherwise, the low types put strictly positive probability on a concession in T, as
waiting until T is less costly. Again, up to a point in time t, there is a positive
probability that an individual concedes in case he has a low cost, and there is a time
period just before T where both individuals are inactive, since they prefer to wait
until T if the cost of the additional waiting time is sufficiently low. Ex ante expected
payoffs are

^e (π_i) = I

n - c_l - ^sf-(c_h - c_l) e- -L

^v^-^cl ^- pH (^t + ^2^ ^-^cl ⁽¹^- ɪnPh⁾)

if T< ^c-^l - cl ɪn ph
if T ≥ ^c-^l - cl ɪn ph

(8)

for i = 1,2.

4 The value of becoming informed

This section considers the decisions on information acquisition in a 2 × 2 game defined
by the payoffs in the war of attrition that have been determined in the previous
section.¹² Let σ⅛ ∈ {N, I} be an individual i’s decision on information where I refers
to information acquisition and N to a decision not to learn one’s own provision cost.

Moreover,

individual i’s ex ante expected payoff in the war

of attrition given the decisions (σi,σj). In case (I, I), for instance, both individuals
have learned their cost of provision, whereas case (N, I) refers to a situation where
exactly one individual has decided to learn his cost. Given σ_j∙, i’s value of information
can be defined as

E.^σ' = E {π^ɔ - E (π^^σ'ɔ .

¹²This approach is employed to simplify the exposition, and it shows that in the equilibrium of
the 2 × 2 game, one player may remain uninformed. The equilibria of the reduced game can also
be supported as Perfect Bayesian equilibria in the analysis of the two-stage game, assuming beliefs
about the rival’s type that do not change with the information acquisition decision (players have
no private information when deciding whether to acquire information).

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Volunteering and the Strategic Value of Ignorance

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