Volunteering and the Strategic Value of Ignorance

Figure 1: Equilibrium information acquisition (for c^ = 2, c_H = 10).

Figure 1 shows the equilibrium outcome for different combinations of T and p_H.
The 45-degree line describes the condition T = c∕2. In the areas B and D, finding
out about the own cost of provision is strictly dominant; in area A, the individuals
prefer to remain uninformed if the rival acquires information, and in equilibrium only
one individual learns his cost (or both individuals randomize their information ac-
quisition decision). In area C, the outcome depends on which equilibrium is selected
in case (N, I). Here, T > c∕2, and for the pure strategy equilibrium, information
acquisition is strictly dominant. For the mixed strategy equilibrium, however, only
one individual acquires information.

A designer’s perspective. There are several dimensions along which efficiency
can be defined. On the one hand, a designer could be interested in the individual
with the lowest cost (highest ability) providing the public good. On the other hand,
the designer might want to minimize the expected waiting time.¹⁷ To capture these
different dimensions, consider the following objective function

W = 2v - X₁E (min {t₁ ,t₂}) - X₂E (k (t₁ ,t₂))

¹⁷In a framework of a contest, a designer may want to induce long times of fighting, i.e. high
waiting times.

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