Optimal Contests with Incomplete Information and Convex Effort Costs
42 Pages Posted: 24 Jan 2020 Last revised: 20 Jun 2022
Date Written: December 31, 2019
Abstract
I investigate the design of effort-maximizing mechanisms when agents have both private information and convex effort costs, and the designer has a fixed prize budget. I first demonstrate that it is always optimal for the designer to utilize a contest with as many participants as possible. Further, I identify a necessary and sufficient 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. Finally, I illustrate how the optimal prize distribution evolves as the contest size grows.
Keywords: contest, incomplete information, convex costs, mechanism design
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