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The optimal multi-stage contest

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  • Fu, Qiang
  • Lu, Jingfeng

Abstract

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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Bibliographic Info

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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Keywords: Contest design; multi-stage contest; Pooling competition;

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References

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  1. 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.
  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. Alexander Matros, 2006. "Elimination Tournaments where Players Have Fixed Resources," Working Papers 205, University of Pittsburgh, Department of Economics, revised Jan 2006.
  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, 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.
  6. Gradstein, Mark & Konrad, Kai A, 1999. "Orchestrating Rent Seeking Contests," Economic Journal, Royal Economic Society, vol. 109(458), pages 536-45, October.
  7. 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.
  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. Skaperdas, Stergios, 1996. "Contest Success Functions," Economic Theory, Springer, vol. 7(2), pages 283-90, February.
  10. Benny Moldovanu & Aner Sela & Xianwen Shi, 2007. "Contests for Status," Journal of Political Economy, University of Chicago Press, vol. 115, pages 338-363.
  11. Rosen, Sherwin, 1986. "Prizes and Incentives in Elimination Tournaments," American Economic Review, American Economic Association, vol. 76(4), pages 701-15, September.
  12. Clark, Derek J & Riis, Christian, 1996. " A Multi-winner Nested Rent-Seeking Contest," Public Choice, Springer, vol. 87(1-2), pages 177-84, April.
  13. Amegashie, J Atsu, 2000. " Some Results on Rent-Seeking Contests with Shortlisting," Public Choice, Springer, vol. 105(3-4), pages 245-53, December.
  14. Konrad, Kai A., 2007. "Strategy in contests: an introduction," Discussion Papers, Research Unit: Market Processes and Governance SP II 2007-01, Social Science Research Center Berlin (WZB).
  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. 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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Citations

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Cited by:
  1. Sheremeta, Roman, 2009. "Contest Design: An Experimental Investigation," MPRA Paper 52101, University Library of Munich, Germany.
  2. Ezra Einy & Ori Haimanko & Diego Moreno & A. Sela & Benyamin Shitovitz, 2013. "Tullock contests with asymmetric information," Economics Working Papers we1314, Universidad Carlos III, Departamento de Economía.
  3. Stracke, Rudi & Höchtl, Wolfgang & Kerschbamer, Rudolf & Sunde, Uwe, 2012. "Optimal Prizes in Dynamic Elimination Contests: An Experimental Analysis," Economics Working Paper Series 1208, University of St. Gallen, School of Economics and Political Science.
  4. Delfgaauw, Josse & Dur, Robert & Non, Arjan & Verbeke, Willem, 2012. "The Effects of Prize Spread and Noise in Elimination Tournaments: A Natural Field Experiment," IZA Discussion Papers 6480, Institute for the Study of Labor (IZA).
  5. Einy, E & Haimanko, O & Moreno, D & Sela, A & Shitovitz, B, 2013. "Tullock Contests with Asymmetric Information," Discussion Papers 2013-11, Graduate School of Economics, Hitotsubashi University.
  6. Ezra Einy & Ori Haimanko & Diego Moreno & Aner Sela & Benyamin Shitovitz, 2013. "Tullock Contests With Asymmetric Information," Working Papers 1303, Ben-Gurion University of the Negev, Department of Economics.
  7. Sheremeta, Roman, 2009. "Essays on Experimental Investigation of Lottery Contests," MPRA Paper 49888, University Library of Munich, Germany.
  8. Konrad, Kai A., 2007. "Strategy in contests: an introduction," Discussion Papers, Research Unit: Market Processes and Governance SP II 2007-01, Social Science Research Center Berlin (WZB).
  9. Aner Sela & Eyal Erez, 2013. "Dynamic contests with resource constraints," Social Choice and Welfare, Springer, vol. 41(4), pages 863-882, October.
  10. Hirata, Daisuke, 2014. "A model of a two-stage all-pay auction," Mathematical Social Sciences, Elsevier, vol. 68(C), pages 5-13.
  11. Kai Konrad & Dan Kovenock, 2012. "Introduction," Economic Theory, Springer, vol. 51(2), pages 241-245, October.
  12. Konrad, Kai A., 2010. "Dynamic contests," Discussion Papers, Research Professorship & Project "The Future of Fiscal Federalism" SP II 2010-10, Social Science Research Center Berlin (WZB).
  13. Maria Arbatskaya & Hugo Mialon, 2010. "Dynamic Multiactivity Contests," Emory Economics 1005, Department of Economics, Emory University (Atlanta).
  14. Stracke, Rudi & Höchtl, Wolfgang & Kerschbamer, Rudolf & Sunde, Uwe, 2014. "Optimal prizes in dynamic elimination contests: Theory and experimental evidence," Journal of Economic Behavior & Organization, Elsevier, vol. 102(C), pages 43-58.
  15. Stracke, Rudi, 2013. "Contest design and heterogeneity," Munich Reprints in Economics 19571, University of Munich, Department of Economics.

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