This paper presents a generalization of the war of attrition, in which effort choices are endogenous. Indeed, in many applications modeled by the war of attrition, such as price wars or military conflicts, agents can expend more or less resources at each instant in time, with important strategic consequences. In the present model, two players are competing for a prize.
Valuations are private information.
Both sides alternate turns in making sunk bids. A player either concedes or matches his opponent s previous bid, in which case he can then overbid. It displays a variety of strategic features depending on players valuations and beliefs. Those features markedly differ from those of the classical war of attrition. The predictions of this theory and the relevance of the new insights are discussed in the context economic examples.