We study a sequential all-pay auction with two contestants who are privately informed about a parameter (ability) that affects their cost of effort. In the model, contestant 1 (the first mover) exerts an effort in the first period which translates into an observable output but with some noise, and contestant 2 (the second mover) observes this noisy output. Then, contestant 2 exerts an effort in the second period, and wins the contest if her output is larger than or equal to the observed noisy output of contestant 1; otherwise, contestant 1 wins. We study two variations of this model where contestant 1 either knows or does not know the realization of the noise before she chooses her effort. Contestant 2 does not know the realization of the noise in both variations. For both variations, we characterize the subgame perfect equilibrium and investigate the effect of a random noise on the expected highest effort in this contest.
