Volunteering and the Strategic Value of Ignorance

Whereas the war of attrition is, in fact, a second-price all-pay auction, Morath and
Münster (2010) study information acquisition in a first-price all-pay auction, but
in their setup, there is no purely strategic value of remaining uninformed. In the
context of winner-pay auctions, incentives to acquire information when decisions are
observable have been shown to depend on the exact auction format and on whether
information is about a private or a common value. An early contribution study-
ing the value of information is Milgrom and Weber (1982); recent work includes
Hernando-Veciana (2009), Larson (2009), and Hernando-Veciana and Trbge (2010).

The next section describes the setup of the model. We analyze in Section 3 the
three different situations that may arise in the volunteering game: no individual has
private information about his provision cost, only one individual is informed, or both
individuals are informed about their cost of provision. In Section 4, we consider the
incentives for information acquisition in a 2 × 2 game defined by the continuation
payoffs in the volunteering game, and we discuss some implications from a designer’s
perspective. Section 5 assesses the robustness of our results. Finally, Section 6
concludes. All proofs are in the appendix.

2 Setup

Consider the following game with two individuals, 1 and 2. One of the two individuals
has to provide a public good of fixed quantity. (We assume that the contribution
that is needed for the provision is indivisible.) The individuals differ with respect to
their cost of provision, denoted by eɪ and C2∙ These cost parameters eɪ and c₂ are
independent draws from a probability distribution that is common knowledge and
assumed to be a discrete function with

c_i ∈ {c_l,c_h} , 0 < c_l <c_h,

and probabilities

Pr(<⅛ = cl) = Pl, Pr(c⅛ = ch)= Ph = 1 - Pl, i = 1, 2.

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