The Generalized War of Attrition

[Forthcoming, American Economic Review.] We model a War of Attrition with N+K firms competing for N prizes. If firms must pay their full costs until the whole game ends, even after dropping out themselves (as in a standard-setting context), each firm's exit time is independent both of K and of other players' actions. If, instead, firms pay no costs after dropping out (as in a natural oligopoly), the field is immediately reduced to N+1 firms. Furthermore, in this limit it is always the K-1 lowest-value firms who drop out in zero time, even though each firm's value is private information to itself.