¤We are grateful to Preston Mc Afee and to three anonymous referees for their many insight-

Abstract: We study a contest with multiple (not necessarily equal) prizes. Ex-ante symmetric, risk-neutral contestants have independently distributed private information about an ability parameter that a¤ects their costs of bidding. The contestant with the highest bid wins the …rst prize, the con-testant with the second-highest bid wins the second prize, and so on until all the prizes are allocated. All contestants incur their respective costs of bidding. The contest’s designer maximizes the expected sum of bids. Our main results are: 1) We display symmetric bidding equilibria for contestants with linear, convex or concave cost functions. 2) If the cost functions are linear or concave, then, it is optimal for the designer to allocate the entire prize sum to a single ”…rst ” prize. 3) We give a necessary and su¢cient condition ensuring that several prizes are optimal if contestants have con-vex cost functions. 4) Even if the designer can use instruments that exclude types with relatively low ability (whose increased bidding cause the bene…t of having more prizes), the award of several prizes is advantageous. ( JEL: D44, J31, D72, D82