to commit to a certain behavior in the war of attrition. Similarly, on an international
level, when governments have to decide whether to provide an international public
good, they can engage experts to provide them with a better estimate of the cost of
provision. But when such investments in information are observable by other play-
ers, investments in information obtain a strategic character. These examples have in
common that the players cannot wait an infinite amount of time before volunteering,
but that there is a time limit on their decision to concede.
We analyze the individuals’ incentives to acquire information about their cost of
provision of a public good in a two-stage game with two individuals. In the first
stage, the individuals can obtain information about their cost of provision. In order
to focus on the strategic considerations, we assume that the information is available
at zero cost. Whether or not an individual decided to find out about his cost can
be observed by the rival before the volunteering game starts. The information that
an individual has obtained, however, is only privately known to this individual. In
the second stage, a volunteering game or war of attrition takes place: the individuals
simultaneously choose a maximum waiting time after which they provide the public
good, given that nobody else has volunteered before. The waiting time until the
public good is provided involves a direct cost. As described above, individuals may
not be able to wait for an infinite amount of time; therefore, we impose a finite
time horizon after which one of the individuals is randomly chosen to pay for the
provision. At some point in time, the dragon may itself decide to attack, or, in the
context of a firm, one employee will be selected by the team leader to perform the
task.
As we will show, the equilibrium of the volunteering game and the incentives to
learn the own cost of provision crucially depend on the length of the time horizon. For
a long time horizon, both individuals prefer to find out about their cost of provision.
If the time horizon of the volunteering game is sufficiently short, individuals without
information about their provision cost prefer a random selection when the time limit
is reached to an early concession. As a consequence, an individual who found out that
his cost would be low may prefer to concede immediately. Therefore, not knowing the
own cost of provision can be advantageous in the volunteering game. For a sufficiently