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.

We show that standard winner‐pay auctions are inept fund‐raising mechanisms because of the positive externality bidders forgo if they top another’s high bid. Revenues are suppressed as a result and remain finite even when bidders value a dollar donated the same as a dollar kept. This problem does not occur in lotteries and all‐pay auctions, where bidders pay irrespective of whether they win. We introduce a general class of all‐pay auctions, rank their revenues, and illustrate how they dominate lotteries and winner‐pay formats. The optimal fund‐raising mechanism is an all‐pay auction augmented with an entry fee and reserve price.