Optimal Contests with Incomplete Information and Convex Effort Costs

42 Pages Posted: 24 Jan 2020 Last revised: 23 Apr 2021

See all articles by Mengxi Zhang

Mengxi Zhang

Institute for Microeconomics, University of Bonn

Date Written: December 31, 2019

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?")

Keywords: contest, incomplete information, convex costs, mechanism design

Suggested Citation

Zhang, Mengxi, Optimal Contests with Incomplete Information and Convex Effort Costs (December 31, 2019). Available at SSRN: https://ssrn.com/abstract=3512155 or http://dx.doi.org/10.2139/ssrn.3512155

Mengxi Zhang (Contact Author)

Institute for Microeconomics, University of Bonn ( email )

Bonn, 53113
Germany

HOME PAGE: http://https://sites.google.com/bu.edu/mengxizhang

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