short time horizon, there are two asymmetric equilibria where one individual finds
out about his cost and the other does not, and one symmetric equilibrium where
both individuals randomize their decision whether to learn their cost. The choice
of the time horizon is an important instrument in influencing the efficiency of the
volunteering game.
The literature on wars of attrition has its origin in applications in biology, model-
ing fights between animals (e.g., Maynard Smith 1974, Riley 1980). Further impor-
tant applications are industrial competition and market exit (Fudenberg and Tirole
1986, Ghemawat and Nalebuff 1985, 1990). The seminal paper that studies the pri-
vate provision of a public good as a war of attrition is Bliss and Nalebuff (1984).
In their setup, the players are privately informed of their cost of provision, and the
equilibrium is efficient in the sense that the player with the lowest cost provides the
public good. The provision of multiple public goods in the framework of a war of
attrition is analyzed by LaCasse et al. (2002) for the case of complete information,
and by Sahuguet (2006) in an environment with private information.3 Bishop and
Cannings (1978), Hendricks et al. (1988), Bilodeau and Slivinski (1996), and Myatt
(2005) study models that exhibit a finite time horizon. We add to this literature
by studying the effects of information on the individuals’ concession times in the
private provision game, and the resulting incentives (not) to become informed. The
strategic considerations involved in the decision on information are similar to the
strategic aspects identified in different settings such as principal-agent relationships
(e.g. Crémer 1995, Kessler 1998): by remaining uninformed, individuals precommit
to a certain behavior in the subsequent interaction.4
Closely related to this paper is work that considers information in auctions.
3Further papers considering wars of attrition with privately informed players are Bulow and
Klemperer (1999), who analyze the case of multiple prizes, and Krishna and Morgan (1997), who
study the case of affiliated signals. Amann and Leininger (1996) consider a general class of all-pay
auctions with private information; the same class of all-pay auctions is analyzed in Riley (1999) for
the case of complete information. Che and Gale (1998) study first-price all-pay auctions with caps
on bidding which are similar to the finite time horizon of the volunteering game assumed here.
4In the context of global warming, Morath (2010) analyzes investments in information in a
standard model of private provision of a continuous public good; the strategic effects that are
present in this paper, however, are driven by the assumption that other countries can observe what
a country has learned.