Sequential all-pay auctions with head starts

We study a sequential all-pay auction with two contestants who are privately informed about a parameter (ability) that affects their cost of effort. We characterize the unique perfect Bayesian equilibrium of this sequential all-pay auction and analyze if giving a head start, i.e., an exogenously determined mechanism that increases the winning probability of the first mover for any level of effort she exerts, improves the contestants’ performance. In particular, we analyze the difference between a multiplicative head start and an additive head start with respect to the effect on the contestants’ performance.