Contest With Incomplete Information: When to Turn up the Heat, and How?

I investigate the optimal design of contests when contestants have both private infor- mation and convex effort costs. The designer has a fixed prize budget and her objective is to maximize the expected total effort. I first demonstrate that it is always optimal for the designer to employ a static, grand all-pay-contest with as many as possible participants. In addition, I identify a sufficient and necessary condition for the winner- takes-all prize structure to be optimal. When this condition fails, the designer may prefer to award multiple prizes of descending sizes. I also provide a characterization of the optimal prize structure for this case. Lastly, I illustrate how the optimal prize structure evolves as contest size grows: the prize structure first becomes more unequal until the optimal level of competition intensity is obtained, and then becomes less unequal to maintain the optimal intensity.