Allocation of prizes in asymmetric all-pay auctions

We study asymmetric all-pay auctions with multiple objects where players' values for the objects are common knowledge. The players have different values for the objects but they have the same ranking. The contest designer may award one-prize including all the objects to the player with the highest effort, or, alternatively, he may allocate several prizes, each prize including one object such that the first prize is awarded to the player with the highest effort, the second prize to the player with the second-highest effort, and so on until all the objects are allocated. We analyze the distribution of effort in one-prize and multiple-prize contests and show that allocation of several prizes may be optimal for a contest designer who maximizes the total effort.