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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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Article provided by Springer 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. Stergios Skaperdas, 1996. "Contest success functions (*)," Economic Theory, Springer, vol. 7(2), pages 283-290.
  2. 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.
  3. 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.
  4. Konrad, Kai A., 2007. "Strategy in contests: an introduction
    [Strategie in Turnieren – eine Einführung]
    ," Discussion Papers, Research Unit: Market Processes and Governance SP II 2007-01, Social Science Research Center Berlin (WZB).
  5. Amegashie, J Atsu, 2000. " Some Results on Rent-Seeking Contests with Shortlisting," Public Choice, Springer, vol. 105(3-4), pages 245-53, December.
  6. Baye, M.R. & Kovenock, D., 1993. "The Solution of the Tullock Rent-Seeking Game when R > 2 : Mixed-Strategy Equilibria and Mean Dissipation Rates," Discussion Paper 1993-68, Tilburg University, Center for Economic Research.
  7. Moldovanu, Benny & Sela, Aner, 1999. "The Optimal Allocation of Prizes in Contests," Sonderforschungsbereich 504 Publications 99-75, Sonderforschungsbereich 504, Universität Mannheim;Sonderforschungsbereich 504, University of Mannheim.
  8. Konrad, Kai A. & Kovenock, Dan, 2006. "Multi-battle contests," Purdue University Economics Working Papers 1187, Purdue University, Department of Economics.
  9. Sherwin Rosen, 1985. "Prizes and Incentives in Elimination Tournaments," NBER Working Papers 1668, National Bureau of Economic Research, Inc.
  10. 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.
  11. Benny Moldovanu & Aner Sela & Xianwen Shi, 2006. "Contests For Status," Working Papers 0604, Ben-Gurion University of the Negev, Department of Economics.
  12. 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.
  13. Gradstein, Mark & Konrad, Kai A, 1999. "Orchestrating Rent Seeking Contests," Economic Journal, Royal Economic Society, vol. 109(458), pages 536-45, October.
  14. Alexander Matros, 2006. "Elimination Tournaments where Players Have Fixed Resources," Working Papers 205, University of Pittsburgh, Department of Economics, revised Jan 2006.
  15. 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.
  16. Rick Harbaugh & Tilman Klumpp, 2004. "Early Round Upsets and Championship Blowouts," Working Papers 2004-09, Indiana University, Kelley School of Business, Department of Business Economics and Public Policy.
  17. 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," Purdue University Economics Working Papers 1039, Purdue University, Department of Economics.
  18. Clark, Derek J & Riis, Christian, 1996. " A Multi-winner Nested Rent-Seeking Contest," Public Choice, Springer, vol. 87(1-2), pages 177-84, April.
  19. 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.
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