Multi Stage Sequential All Pay Auctions

Abstract: 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. Contestants arrive one by one and observe the efforts of all contestants before them. We characterize the Perfect Bayesian equilibrium of these multi-stage sequential all-pay contests and analyze the effect of the number of contestants and their types on the contestants' effort. For the two players case we also 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’ efforts. Finally we analyze the effect of noise in the observability of the effort of the first player on the contestants’ efforts.