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 whether his rival has a head start, i.e., an initial advantage in the auction. The game has a unique Bayesian Nash equilibrium outcome whose shape depends on the expected head start. In equilibrium, the potentially stronger player generates an informational rent if and only if her potential head start occurs with high probability or is sufficiently high. This result differs from the case of uncertainty about cost or valuation of the opponent, in which the potentially stronger player always obtains an informational rent. JEL classification: C72, C73