The value of information in asymmetric all-pay auctions

This note 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 of the head start. The stronger player generates an informational rent if and only if his head start distribution is not stochastically dominated by a uniform distribution. I identify why my results for an uncertain head start differ qualitatively from uncertainty about a cost function or a valuation.