The optimal allocation of prizes in contests

We study a contest with multiple, nonidentical prices. Participants are privately informed about a parameter (ability) affecting their costs of effort. The contestant with the highest effort wins the first prize, the contestant with the second-highest effort wins the second prize, and so on until all the prizes are allocated. The contest's designer maximizes expected effort. Where cost functions are linens or concave in effort it is optimal to allocate the entire prize sum to a single "first" prize. When cost functions are convex, several positive prizes may be optimal.