payoff functions are given by
{v — tj, ti > tj
V — '^ — ti, ti = tj , i = 1,2.
(1)
v — Ci — ti, ti < tj
For all possible tɪ and t2, the public good is provided, and its value V to the individuals
is assumed to be the same for both individuals and independent of the provision time.
The idiosyncrasies are captured by the provision cost. The individual who chooses
the lower waiting time has to bear the provision cost, and both individuals have to
pay the cost of waiting, determined by the minimum of tɪ and t2. If both individuals
decide not to concede before T, that is tɪ = t2 = T, one of them is randomly
selected to provide the public good, and their expected payoff in this case is equal
to V — ci∕2 — T.
3 The volunteering game
This section analyzes the war of attrition in isolation, fixing the decisions on informa-
tion acquisition. The equilibrium concept is Bayesian Nash equilibrium. Whenever
players are symmetric in the sense that both have (have not) acquired information,
the analysis will focus on symmetric equilibria of the war of attrition.7
In the war of attrition, the individuals choose their time of concession ti, know-
ing the decisions on information. The time horizon T affects the properties of the
equilibrium of the war of attrition for all possible stage 1 decisions. Compared to a
provision in ti < T, individuals can reduce their expected cost of provision by wait-
ing until T and then possibly being subject to a random selection. This trade-off
between lower expected provision cost and higher cost of waiting generates a time
interval before T in which, in equilibrium, there is zero probability that an individual
volunteers.
7In the next section, decisions on information acquisition will be considered in a 2 x 2 game
defined by the payoffs in the war of attrition for the respective information structure.