We study all-pay auctions with a single object.
Bidders have private information about the value of the object.
We show that regardless of the number of bidders if bidders have linear or concave cost functions then setting an upper bound on the bids is not profitable for the seller. On the other hand, if bidders have convex cost functions and the number of bidders is sufficiently large, then setting the optimal upper bound on the bids is profitable for the seller.