The paper analyzes the optimal allocation of prizes in contests with multiple, possibly unequal, prizes. Contestants have private information about their ability, which affects their cost of bidding. The contestant with the highest bid wins the first prize, the second-highest bid wins the second prize, and so on. The contest designer aims to maximize the expected sum of bids. The main findings are: 1) Bidding equilibria are derived for any number of contestants with linear, concave, or convex cost functions and any ability distribution. 2) If cost functions are linear or concave, it is optimal for the designer to allocate the entire prize sum to a single "first" prize, regardless of ability distribution. 3) Necessary and sufficient conditions are provided for when multiple prizes are optimal if contestants have convex cost functions. The paper discusses various contest scenarios, including rent-seeking, R&D rivalry, sports, arms races, and job promotions. It highlights the importance of understanding how prize allocation affects bidding behavior, especially when contestants have different abilities and cost structures. The study shows that for linear or concave cost functions, a single first prize is optimal, while for convex cost functions, multiple prizes may be optimal depending on the number of contestants and ability distribution. The results are illustrated with examples and mathematical derivations, emphasizing the role of ability distribution and cost functions in determining optimal prize structures. The paper concludes that the optimal prize structure depends on the number of contestants, ability distribution, and the form of the cost function.The paper analyzes the optimal allocation of prizes in contests with multiple, possibly unequal, prizes. Contestants have private information about their ability, which affects their cost of bidding. The contestant with the highest bid wins the first prize, the second-highest bid wins the second prize, and so on. The contest designer aims to maximize the expected sum of bids. The main findings are: 1) Bidding equilibria are derived for any number of contestants with linear, concave, or convex cost functions and any ability distribution. 2) If cost functions are linear or concave, it is optimal for the designer to allocate the entire prize sum to a single "first" prize, regardless of ability distribution. 3) Necessary and sufficient conditions are provided for when multiple prizes are optimal if contestants have convex cost functions. The paper discusses various contest scenarios, including rent-seeking, R&D rivalry, sports, arms races, and job promotions. It highlights the importance of understanding how prize allocation affects bidding behavior, especially when contestants have different abilities and cost structures. The study shows that for linear or concave cost functions, a single first prize is optimal, while for convex cost functions, multiple prizes may be optimal depending on the number of contestants and ability distribution. The results are illustrated with examples and mathematical derivations, emphasizing the role of ability distribution and cost functions in determining optimal prize structures. The paper concludes that the optimal prize structure depends on the number of contestants, ability distribution, and the form of the cost function.