An analysis of the two-bidder all-pay auction with common values

Abstract

This paper studies a symmetric two-bidder all-pay auction where the bidders compete for a prize whose unknown common value is either high or low. The bidders’ private signals (or types) are discrete and affiliated through the value. Even with affiliated signals, monotonicity of equilibria can fail in the sense that the bidder with a higher signal does not always win the auction. I show that when monotonicity fails, there exist multiple symmetric equilibria but the bidder’s type-dependent payoff is invariant across the equilibria. The paper provides a closed-form formula for the equilibrium payoffs and a condition for rent dissipation.