Volunteering and the Strategic Value of Ignorance

Ci        if  t₁ < t₂

(eɪ + C2) /2  if  ti = t2

C2        if  ti > t2

is the (expected) cost of providing the public good and Λ_i and A₂ are the weights
given to the expected waiting time and the expected provision cost. We assume that
the designer does not know the individuals’ cost of provision and cannot change the
structure of the game.

Suppose first that A_i = 0 and A₂ > 0, that is, maximizing W is equivalent
to minimizing the expected cost of provision, E (к (t_i,t₂)). Here, W is highest if
both individuals acquire information (case (I, I)) and an individual with low cost
volunteers with probability one before the time limit is reached. This implies that
T > c_l∕2 — Cl Inрн (by Lemma 4) and T > T (by Proposition 1). In this case,
information acquisition is efficient.

Remark 1 If the designer wants to minimize the expected cost of provision, a suf-
ficiently high time limit ensures both efficient information acquisition and efficient
provision of the public good.

Another objective could be to focus on the expected waiting time. Let A₂ = 0.
Obviously, if A_i > 0, the time horizon should be as short as possible, and W is
maximized for T = 0. In this case, the decisions on information become irrelevant.¹⁸

If the designer takes into account both the expected cost of provision and the
expected waiting cost, a benevolent designer may want to maximize the individuals’
expected payoffs, which is equivalent to A_i = 2 and A₂ = 1. Then, T = 0 need not be

¹⁸If T > c/2 and in case (N, I) the pure strategy is selected, W would also be maximized if
exactly one individual acquires information. This, however, does not occur in equilibrium if the
individuals decide on information acquisition, but only if information acquisition is forbidden for
one individual. In this sense, there can be too much information acquisition in equilibrium if λ₁ > 0
and λ₂ = 0. If instead λ₁ < 0 and the designer wants to maximize the expected waiting time, the
waiting times are highest if T > c/2 and none of the individuals acquires information. Thus, it
would be optimal to prohibit information acquisition.

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