In this paper, we study score procurement auctions with all-pay quality bids. A supplier's score is the difference between his quality and price bids. The supplier with the highest score wins and gets paid his own price bid. The procurer's payoff is the difference between the winner's quality...

We characterize the unique Markov perfect equilibrium of a tug-of-war without exogenous noise, in which players have the opportunity to engage in a sequence of battles in an attempt to win the war. Each battle is an all-pay auction in which the player expending the greater resources wins. In...

We characterize the unique Markov perfect equilibrium of a tug-of-war without exogenous noise, in which players have the opportunity to engage in a sequence of battles in an attempt to win the war. Each battle is an all-pay auction in which the player expending the greater resources wins. In...