We consider a two-player all-pay auction with symmetric independent private values that are uniformly distributed. The designer chooses the size of a head start that is given to one of the players. The designer’s objective is to maximize a convex combination of the expected highest effort and...

This paper proposes an extension of the valuation equilibrium concept (Jehiel and Samet, 2007), which partly endogenises the underlying grouping of actions. The effect on equilibrium predictions is illustrated in a burning money game.