Contest Design as a Risk Averse Bidder Problem

Abstract

I investigate the optimal design of contests when contestants have both private information 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 grand static contest with as many participants as possible. Further, 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 allocation rule for this case. Lastly, I illustrate how the optimal prize distribution evolves as contest size grows: the prize distribution first becomes more unequal until the optimal level of competition intensity is obtained and then becomes less unequal to maintain the optimal intensity. (A previous version has been circulated under the title Contest with Incomplete Information: When to Turn Up the Heat, and How?)