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The Optimal Multi-Stage Contest

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  • Qiang Fu
  • JingFeng Lu

Abstract

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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Paper provided by www.najecon.org 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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References

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  1. Alexander Matros, 2006. "Elimination Tournaments where Players Have Fixed Resources," Working Papers 205, University of Pittsburgh, Department of Economics, revised Jan 2006.
  2. Rosen, Sherwin, 1986. "Prizes and Incentives in Elimination Tournaments," American Economic Review, American Economic Association, vol. 76(4), pages 701-15, September.
  3. 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.
  4. 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.
  5. 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).
  6. 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.
  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. 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.
  9. 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.
  10. 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.
  11. Gradstein, Mark & Konrad, Kai A, 1999. "Orchestrating Rent Seeking Contests," Economic Journal, Royal Economic Society, vol. 109(458), pages 536-45, October.
  12. 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.
  13. Clark, Derek J & Riis, Christian, 1996. " A Multi-winner Nested Rent-Seeking Contest," Public Choice, Springer, vol. 87(1-2), pages 177-84, April.
  14. Amegashie, J Atsu, 2000. " Some Results on Rent-Seeking Contests with Shortlisting," Public Choice, Springer, vol. 105(3-4), pages 245-53, December.
  15. Skaperdas, Stergios, 1996. "Contest Success Functions," Economic Theory, Springer, vol. 7(2), pages 283-90, February.
  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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Cited by:
  1. Maria Arbatskaya & Hugo Mialon, 2010. "Dynamic Multiactivity Contests," Emory Economics 1005, Department of Economics, Emory University (Atlanta).
  2. 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.
  3. 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).
  4. Sheremeta, Roman, 2009. "Contest Design: An Experimental Investigation," MPRA Paper 52101, University Library of Munich, Germany.
  5. 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).
  6. Kai Konrad & Dan Kovenock, 2012. "Introduction," Economic Theory, Springer, vol. 51(2), pages 241-245, October.
  7. Stracke, Rudi & Höchtl, Wolfgang & Kerschbamer, Rudolf & Sunde, Uwe, 2013. "Optimal Prizes in Dynamic Elimination Contests: An Experimental Analysis," Munich Reprints in Economics 19572, University of Munich, Department of Economics.
  8. Stracke, Rudi, 2013. "Contest design and heterogeneity," Munich Reprints in Economics 19571, University of Munich, Department of Economics.
  9. Aner Sela & Eyal Erez, 2013. "Dynamic contests with resource constraints," Social Choice and Welfare, Springer, vol. 41(4), pages 863-882, October.
  10. Rudi Stracke & Wolfgang Höchtl & Rudolf Kerschbamer & Uwe Sunde, 2014. "Optimal prizes in dynamic elimination contests: Theory and experimental evidence," Working Papers 2014-08, Faculty of Economics and Statistics, University of Innsbruck.
  11. 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.
  12. Hirata, Daisuke, 2014. "A model of a two-stage all-pay auction," Mathematical Social Sciences, Elsevier, vol. 68(C), pages 5-13.
  13. 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).
  14. Sheremeta, Roman, 2009. "Essays on Experimental Investigation of Lottery Contests," MPRA Paper 49888, University Library of Munich, Germany.
  15. 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.

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