This paper studies the optimal contest design problem when the abilities of
the risk neutral contestants are independent private information. The
contest designer has a fixed prize budget to elicit efforts from the
contestants. We consider all possible mechanisms that allocate prizes and
punishments (negative prizes) across the contestants. We find that an
optimal contest mechanism does not exist. Nevertheless, the utmost total
efforts (i.e. highest efforts inducible when all contestants are of the highest
possible ability) can almost be achieved by mechanisms involving exploding
punishments. When there is a bound on the punishment (i.e. $K$), an optimal
contest mechanism exists and can be implemented by a modified all-pay
auction with a minimum bid and a single prize consisting of the entire prize
budget augmented by an entry fee of $K$ from each participant; when no one
bids, all participants share a nonnegative prize equally.