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The optimal multi-stage contest

  • Fu, Qiang
  • Lu, Jingfeng

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 University Library of Munich, Germany in its series MPRA Paper with number 946.

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Date of creation: Nov 2006
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Handle: RePEc:pra:mprapa:946
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  1. Baye, M.R. & Kovenock, D. & De Vries, C.G., 1991. "Rigging The Lobbying Process: An Application Of The All- Pay Auction," Purdue University Economics Working Papers 1002, Purdue University, Department of Economics.
  2. Konrad, Kai A. & Kovenock, Dan, 2006. "Multi-battle contests," Purdue University Economics Working Papers 1187, Purdue University, Department of Economics.
  3. Sherwin Rosen, 1985. "Prizes and Incentives in Elimination Tournaments," NBER Working Papers 1668, National Bureau of Economic Research, Inc.
  4. Amegashie, J Atsu, 2000. " Some Results on Rent-Seeking Contests with Shortlisting," Public Choice, Springer, vol. 105(3-4), pages 245-53, December.
  5. 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.
  6. 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.
  7. Skaperdas, Stergios, 1996. "Contest Success Functions," Economic Theory, Springer, vol. 7(2), pages 283-90, February.
  8. 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.
  9. Alexander Matros, 2006. "Elimination Tournaments where Players Have Fixed Resources," Working Papers 205, University of Pittsburgh, Department of Economics, revised Jan 2006.
  10. 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.
  11. 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.
  12. 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.
  13. Rick Harbaugh & Tilman Klumpp, 2005. "Early Round Upsets and Championship Blowouts," Economic Inquiry, Western Economic Association International, vol. 43(2), pages 316-329, April.
  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. 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).
  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. 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.
  18. Gradstein, Mark & Konrad, Kai A, 1999. "Orchestrating Rent Seeking Contests," Economic Journal, Royal Economic Society, vol. 109(458), pages 536-45, October.
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