We study a contest with multiple, nonidentical prices. Participants are pri
vately informed about a parameter (ability) affecting their costs of effort
. The contestant with the highest effort wins the first prize, the contesta
nt with the second-highest effort wins the second prize, and so on until al
l the prizes are allocated. The contest's designer maximizes expected effor
t. Where cost functions are linens or concave in effort it is optimal to al
locate the entire prize sum to a single "first" prize. When cost functions
are convex, several positive prizes may be optimal.