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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 with pooling competition in each stage. We allow the contest organizer to design the contest structure in two arms: contest sequence (the number of stages, and the number of remaining contestants in each stage), and prize allocation. First, we find that the optimality of "winner-take-all" (single final winner, single final prize, no intermediate prizes) is independent of the contest sequence. Second, we show that the more complete the contest sequence is, the more efforts can be induced from the contestants. Therefore, the optimal contest eliminates one contestant at each stage until the finale, while a single winner takes over the entire prize purse. Our results not only rationalize various forms of multi-stage contests conducted in reality, such as the well-known Fox TV show "American Idol", but also shed light on the design of internal organizational hierarchy.

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Paper provided by in its series NajEcon Working Paper Reviews with number 843644000000000387.

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Date of creation: 17 Aug 2007
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Handle: RePEc:cla:najeco:843644000000000387
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  1. Sherwin Rosen, 1985. "Prizes and Incentives in Elimination Tournaments," NBER Working Papers 1668, National Bureau of Economic Research, Inc.
  2. 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.
  3. 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.
  4. Konrad, Kai A. & Kovenock, Dan, 2006. "Multi-Battle Contests," CEPR Discussion Papers 5645, C.E.P.R. Discussion Papers.
  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. 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).
  7. 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.
  8. Moldovanu, Benny & Sela, Aner & Shi, Xianwen, 2005. "Contests for Status," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 139, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
  9. Alexander Matros, 2006. "Elimination Tournaments where Players Have Fixed Resources," Working Papers 205, University of Pittsburgh, Department of Economics, revised Jan 2006.
  10. 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.
  11. 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.
  12. Gradstein, Mark & Konrad, Kai A, 1999. "Orchestrating Rent Seeking Contests," Economic Journal, Royal Economic Society, vol. 109(458), pages 536-45, October.
  13. Baye, M.R. & Kovenock, D. & De Vries, C.G., 1992. "Rigging the Lobbying Process: An Application of the All- Pay Auction," Papers 9-92-2, Pennsylvania State - Department of Economics.
  14. 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.
  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. 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.
  17. Stergios Skaperdas, 1996. "Contest success functions (*)," Economic Theory, Springer, vol. 7(2), pages 283-290.
  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. 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.
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