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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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Bibliographic Info

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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Related research

Keywords: Multi-stage contest; Effort maximization; Prize allocation; Winner-take-all; Sequential elimination; C7; D7; J3;

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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. 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.
  3. Rick Harbaugh & Tilman Klumpp, 2005. "Early Round Upsets and Championship Blowouts," Economic Inquiry, Western Economic Association International, vol. 43(2), pages 316-329, April.
  4. 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.
  5. 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.
  6. Benny Moldovanu & Aner Sela & Xianwen Shi, 2007. "Contests for Status," Journal of Political Economy, University of Chicago Press, vol. 115, pages 338-363.
  7. Skaperdas, Stergios, 1996. "Contest Success Functions," Economic Theory, Springer, vol. 7(2), pages 283-90, February.
  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. 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.
  10. Rosen, Sherwin, 1986. "Prizes and Incentives in Elimination Tournaments," American Economic Review, American Economic Association, vol. 76(4), pages 701-15, September.
  11. Amegashie, J Atsu, 2000. " Some Results on Rent-Seeking Contests with Shortlisting," Public Choice, Springer, vol. 105(3-4), pages 245-53, December.
  12. 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.
  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. Gradstein, Mark & Konrad, Kai A, 1999. "Orchestrating Rent Seeking Contests," Economic Journal, Royal Economic Society, vol. 109(458), pages 536-45, October.
  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. 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. 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).
  2. 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.
  3. 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.
  4. Aner Sela & Eyal Erez, 2013. "Dynamic contests with resource constraints," Social Choice and Welfare, Springer, vol. 41(4), pages 863-882, October.
  5. Roman M. Sheremeta, 2009. "Contest Design: An Experimental Investigation," Working Papers 09-05, Chapman University, Economic Science Institute.
  6. Maria Arbatskaya & Hugo Mialon, 2010. "Dynamic Multiactivity Contests," Emory Economics 1005, Department of Economics, Emory University (Atlanta).
  7. 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.
  8. Hirata, Daisuke, 2014. "A model of a two-stage all-pay auction," Mathematical Social Sciences, Elsevier, vol. 68(C), pages 5-13.
  9. 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.
  10. Kai Konrad & Dan Kovenock, 2012. "Introduction," Economic Theory, Springer, vol. 51(2), pages 241-245, October.
  11. Stracke, Rudi, 2013. "Contest design and heterogeneity," Munich Reprints in Economics 19571, University of Munich, Department of Economics.
  12. 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.
  13. Sheremeta, Roman, 2009. "Essays on Experimental Investigation of Lottery Contests," MPRA Paper 49888, University Library of Munich, Germany.
  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. 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).

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