Volunteering and the Strategic Value of Ignorance

Lost opportunity of provision at T. The provision of many public goods is
allocated on a voluntary basis, but it is compulsory in the sense that one individual
has to contribute. In companies, for instance, a team leader may select one individual
if no one volunteers. Other public goods can only be provided within a certain period,
after which the opportunity of provision disappears.

Instead of assuming that at T one individual is randomly selected, suppose that
the investment opportunity disappears if no individual has conceded before T. In this
case, the incentive to wait until T in the war of attrition is weakened; the analysis,
however, qualitatively carries over from the previous section if we modify Assumption
1 on the time limit such that individuals with a high cost do not want to provide
the public good and individuals with a low cost prefer to concede. This requires the
time limit to be such that:

Assumption 1’ 0 < — (n — ⅛) < T < — (n — c∏).

Hence, high types have a (weakly) dominant strategy to wait until T. Moreover,
if T is sufficiently small (T < — (n — c)) and only individual j knows his contribution
cost, the uninformed individual i waits until T (as in Lemma 3a). For a larger T,
there is an equilibrium where i and jɪ, randomize on some interval [0, t∖ U{T} (similar
to Lemma 3b(ii)) and j_L has a mass point at zero.

Proposition 4 Consider the game of information acquisition and suppose that at T
the opportunity of provision disappears. If Assumption 1’ holds and T is sufficiently
small, only one individual acquires information in equilibrium.

We do not provide a complete analysis of equilibria of the war of attrition²² and
incentives to acquire information, but we show that, whenever T is small, there is a
strategic value of ignorance: as in the previous section, remaining uninformed can be
used as a commitment not to concede if an individual’s expected cost of provision is
sufficiently high in relation to the payoff from waiting until T.

²²A detailed analysis of equilibria of the war of attrition would build on Theorems 1-3 in Hendricks
et al. (1988).

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