Description:
This paper analyzes a two-player all-pay auction with incomplete information. More precisely, one bidder is uncertain about the size of the initial advantage of his rival modeled as a head start in the auction. I derive the unique Bayesian Nash equilibrium outcome for a large class of cumulative distribution functions over head starts. In equilibrium, the stronger player generates an informational rent if and only if his head start distribution is not stochastically dominated by a uniform distribution. This result introduces a new perspective on lobbying contests and procurement contests.