The winner-take-all nature of all-pay auctions makes the outcome sensitive to decision errors, which we introduce with a logit formulation. The equilibrium bid distribution is a fixed point: the belief distributions that determine expected payoffs equal the choice distributions determined by expected payoffs. We prove existence, uniqueness, and symmetry properties. In contrast to the Nash equilibrium, the comparative statics of the logit equilibrium are intuitive: rent dissipation increases with the number of players and the bid cost. Overdissipation of rents is impossible under full rationality but is observed in laboratory experiments. Our model predicts this property.