Volunteering and the Strategic Value of Ignorance

Moreover,

с := PlCl + Phc_h

is an individual’s expected cost of provision. At the beginning of the game, the
individuals know neither their own cost of provision nor their rival’s cost, but only
that this cost can be high or low, and the corresponding probabilities.⁵

In stage 1 of the game, the individuals can find out about their own provision cost:
if an individual decides to become informed, he privately observes his provision cost.
Information acquisition does not involve any direct cost, and the decisions whether
or not to obtain information are made simultaneously and become commonly known
at the end of stage 1.

In stage 2, the individuals i = 1, 2 simultaneously choose a time of concession
t_i, i.e., individual i plans to provide the public good in t_i if individual j = i has
not volunteered before ⅞. As soon as one individual volunteers, the game ends.
However, there is a maximum waiting time T which is exogenously given and common
knowledge. Thus, the strategy space is restricted to t_i ∈ [0,T]. If both individuals
volunteer exactly at the same time, the provision of the public good is allocated
with equal probability to the individuals. Waiting involves a direct cost to both
individuals, which is assumed to be linear in the waiting time.⁶ Stage 2 is strategically
equivalent to the war of attrition or second-price all-pay auction with a cap on
bidding.

Denoting by v an individual’s utility from the provision of the public good, the

⁵The assumption of a discrete distribution determines the structure of the equilibrium strategies
in the war of attrition if at least one individual learned his cost. The result on incentives to become
informed qualitatively carries over to the case where the individuals’ cost is drawn from a continuous
distribution. See the discussion in the concluding section.

⁶If the individuals have identical and strictly increasing cost functions Ъ (t_i) for the waiting time
ti, the analysis can be carried out in a similar way by employing ki = Ъ (ti) as choice variable.

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