Multi-stage sequential all-pay auctions

•We study an all-pay auction with n players who exert efforts sequentially.•Each player׳s cost of effort is his private information.•A player observes all efforts of preceding players.•We show that the expected highest effort is non-monotonic in the number of players.•We show that a set of weak players may yield a higher expected highest effort than a set of strong players.

We study multi-stage sequential all-pay contests (auctions) where heterogeneous contestants are privately informed about a parameter (ability) that affects their cost of effort. We characterize the perfect Bayesian equilibrium of these contests and analyze the effect of the number of contestants and their types on the contestants׳ expected highest effort.