acquisition is strictly dominant for T > T, and both individuals will acquire infor-
mation. For T < T, however, if individual 1 acquires information, 2 will remain
uninformed, and vice-versa.
Proposition 2 Suppose that decisions on information take place sequentially and
Assumption 1 holds. If the time horizon is sufficiently small, the first mover will
decide to remain uninformed, and the second mover will acquire information.
Whenever T < c/2 and exactly one individual has acquired information, the
payoff of the uninformed individual is higher than the payoff of the informed indi-
vidual. Thus, individuals prefer to be the uninformed player. If T > c/2, we have to
distinguish which equilibrium is selected in case (^ I). For the mixed strategy equi-
librium, a strategic incentive to remain uninformed exists, and an increasing time
horizon T makes it less attractive to remain uninformed. There is, however, a range
of parameters T where the strategic advantage from being uninformed is sufficiently
high such that a first mover would choose to remain uninformed.
Information about a common value. In the previous section, we have identified
a strategic value of ignorance in situations where information about a private value
can be obtained. If the information is about some component which is common to all
individuals, a similar strategic incentive is present. Consider the extreme case of a
pure common value and suppose that the individuals’ costs of provision are perfectly
correlated. Thus, if an individual has acquired information, he knows not only his
own type, but also his rival’s type.
In the war of attrition, if no individual has acquired information, the analysis does
not change. Moreover, if both individuals have acquired information, they randomize
their concession time if they both have a low cost, and they wait until T if they both
have a high cost.
If exactly one individual knows the cost of provision and T < c/2, the equilibrium
of the war of attrition is similar to the one characterized in Lemma 3a. Here, if the
informed individual j does not concede immediately, the uninformed individual i
22