Abstract
This paper investigates the optimal (effort-maximizing) structure of multi-stage sequential-elimination contests. We allow the contest organizer to design the contest structure using two instruments: contest sequence (the number of stages, and the number of contestants remaining after each stage), and prize allocation. When the contest technology is sufficiently noisy, we find that multi-stage contests elicit more effort than single-stage contests. For concave and moderately convex impact functions, the contest organizer should allocate the entire prize purse to a single final prize, regardless of the contest sequence. Additional stages always increase total effort. Therefore, the optimal contest eliminates one contestant at each stage until the finale when a single winner obtains the entire prize purse. Our results thus rationalize various forms of multi-stage contests that are conducted in the real world.
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We owe special thanks to Kyung Hwan Baik for the very inspiring discussion. The paper has tremendously benefited from the constructive comments and suggestions provided by an anonymous referee and coeditor Dan Kovenock. We are grateful to Atsu Amegashie, Michael Baye, Indranil Chakaraborty, Jimmy Chan, Jiahua Che, Yeon-Koo Che, John Conlon, Sudipto Dasgupta, Jeff Ely, Hanming Fang, Yuk-Fai Fong, Qiang Gong, Tanjim Hossain, Xinyu Hua, Kai Konrad, Tilman Klumpp, Lawrance Martin, Johannes Münster, Benny Moldovanu, Marco Ottaviani, Ivan Png, Aner Sela, Curtis Taylor, Lixin Ye, Hussein Yildrim, Hongjun Zhong and Wen Zhou. We would like to acknowledge the helpful comments and suggestions made by participants of 2006 Midwest Economic Theory Meeting, the 2006 PET conference, the 2007 SET conference, the 2008 Young Research Workshop on Contests (WZB, Berlin), the 2008 CESifo Venice Workshop on Contests, and the 2008 HKUST IO Workshop. The authors gratefully acknowledge the financial support from National University of Singapore [R-313-000-068-112 (Q. Fu) and R-122-000-108-112 (J. Lu)].
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Fu, Q., Lu, J. The optimal multi-stage contest. Econ Theory 51, 351–382 (2012). https://doi.org/10.1007/s00199-009-0463-z
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DOI: https://doi.org/10.1007/s00199-009-0463-z