Perfectly discriminating contests (or all pay auction) are widely used as a model of situations where individuals devote resources to win some prize. In reality such contests are often preceded by investments of the contestants into their ability to fight in the contest. This paper studies a two...

We investigate a version of the classic Colonel Blotto game in which individual battles may have different values. Two players allocate a fixed budget across battlefields and each battlefield is won by the player who allocates the most to that battlefield. The winner of the game is the player...

We consider imperfectly discriminating, common-value, all-pay auctions (or contests) where some players know the value of the prize, others do not. We show that if the prize is always of positive value, then all players are active in equilibrium. If the prize is of value zero with positive...