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The optimal multi-stage contest

  • Qiang Fu

    ()

  • Jingfeng Lu

    ()

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. Copyright Springer-Verlag 2012

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File URL: http://hdl.handle.net/10.1007/s00199-009-0463-z
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Article provided by Springer & Society for the Advancement of Economic Theory (SAET) in its journal Economic Theory.

Volume (Year): 51 (2012)
Issue (Month): 2 (October)
Pages: 351-382

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Handle: RePEc:spr:joecth:v:51:y:2012:i:2:p:351-382
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  1. Konrad, Kai A. & Kovenock, Dan, 2006. "Multi-Battle Contests," CEPR Discussion Papers 5645, C.E.P.R. Discussion Papers.
  2. Baye, Michael R & Kovenock, Dan & de Vries, Casper G, 1993. "Rigging the Lobbying Process: An Application of the All-Pay Auction," American Economic Review, American Economic Association, vol. 83(1), pages 289-94, March.
  3. Benny Moldovanu & Aner Sela, 2001. "The Optimal Allocation of Prizes in Contests," American Economic Review, American Economic Association, vol. 91(3), pages 542-558, June.
  4. Rick Harbaugh & Tilman Klumpp, 2005. "Early Round Upsets and Championship Blowouts," Economic Inquiry, Western Economic Association International, vol. 43(2), pages 316-329, April.
  5. Baye, M.R. & Kovenock, D. & De Vries, C.G., 1993. "The Solution to the Tullock Rent-Seeking Game when R > 2: Mixed Strategy Equilibria and Mean Dissipation Rates," Papers 10-93-9, Pennsylvania State - Department of Economics.
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  7. Stergios Skaperdas, 1996. "Contest success functions (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 7(2), pages 283-290.
  8. Amegashie, J Atsu, 2000. "Some Results on Rent-Seeking Contests with Shortlisting," Public Choice, Springer, vol. 105(3-4), pages 245-53, December.
  9. Konrad, Kai A., 2007. "Strategy in contests: an introduction
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  10. Gradstein, Mark & Konrad, Kai A, 1999. "Orchestrating Rent Seeking Contests," Economic Journal, Royal Economic Society, vol. 109(458), pages 536-45, October.
  11. Benny Moldovanu & Aner Sela & Xianwen Shi, 2006. "Contests For Status," Working Papers 0604, Ben-Gurion University of the Negev, Department of Economics.
  12. Baye, Michael R & Kovenock, Dan & de Vries, Casper G, 1999. "The Incidence of Overdissipation in Rent-Seeking Contests," Public Choice, Springer, vol. 99(3-4), pages 439-54, June.
  13. Clark, Derek J & Riis, Christian, 1998. "Competition over More Than One Prize," American Economic Review, American Economic Association, vol. 88(1), pages 276-89, March.
  14. Barut, Yasar & Kovenock, Dan, 1998. "The symmetric multiple prize all-pay auction with complete information," European Journal of Political Economy, Elsevier, vol. 14(4), pages 627-644, November.
  15. Clark, Derek J. & Riis, Christian, 1998. "Influence and the discretionary allocation of several prizes," European Journal of Political Economy, Elsevier, vol. 14(4), pages 605-625, November.
  16. Clark, Derek J & Riis, Christian, 1996. "A Multi-winner Nested Rent-Seeking Contest," Public Choice, Springer, vol. 87(1-2), pages 177-84, April.
  17. Sherwin Rosen, 1985. "Prizes and Incentives in Elimination Tournaments," NBER Working Papers 1668, National Bureau of Economic Research, Inc.
  18. Richard L. Fullerton & R. Preston McAfee, 1999. "Auctioning Entry into Tournaments," Journal of Political Economy, University of Chicago Press, vol. 107(3), pages 573-605, June.
  19. Amegashie, J Atsu, 1999. "The Design of Rent-Seeking Competitions: Committees, Preliminary and Final Contests," Public Choice, Springer, vol. 99(1-2), pages 63-76, April.
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