Volunteering and the Strategic Value of Ignorance



optimal: if T is only slightly larger than c^2, one individual acquires information,
and he concedes immediately in case he has a low cost. The gain from the decrease
in the expected provision cost (due to information acquisition) outweighs the higher
waiting cost if
pH is sufficiently small and/or cH is large, and it can be optimal to
choose an intermediate time limit such that individuals have an incentive to acquire
information and to choose an early concession if they have a low provision cost.
Similarly, it can be desirable that both individuals acquire information. In the latter
case (case
(/, I)), the sum of expected payoffs is highest if T = c^2 c^ InpH such
that individuals with low cost concede before
T with probability one. Higher T do
not change the efficiency of the provision (captured by
к (H,⅛)), but increase the
waiting cost given that both individuals have a high cost. In general, the optimal
choice of
T depends on the balancing of expected waiting time and cost of provision
and on the probability of facing individuals with a high cost of provision.

Remark 2 If the designer wants to maximize the sum of expected payoffs, the trade-
off between efficiency of the provision and cost of waiting makes an intermediate time
limit optimal whenever p
H is sufficiently small and/or cH is large.

5 Extensions

Sequential decisions on information. Whenever there is an incentive to remain
uninformed, this can cause a coordination problem. When individuals randomize
their information acquisition decision, they may acquire too much or too little infor-
mation from their own point of view. Considering sequential choices on information
can mitigate this coordination problem, and it will reflect, for instance, situations
where individuals can, one after the other, ask questions about a task that has to be
performed.

Suppose that decisions on information take place sequentially: individual 1 de-
cides first, and individual
2 moves second.19 As stated in Proposition 1, information

19We do not discuss the question of endogenous timing of information acquisition decisions.

21



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