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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. 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.
  2. Skaperdas, Stergios, 1996. "Contest Success Functions," Economic Theory, Springer, vol. 7(2), pages 283-90, February.
  3. 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.
  4. Michael R. Baye & Dan Kovenock & Casper G. de Vries, 1997. "The Incidence of Overdissipation in Rent-Seeking Contests," Tinbergen Institute Discussion Papers 97-045/2, Tinbergen Institute.
  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. 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.
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  8. Clark, Derek J & Riis, Christian, 1996. " A Multi-winner Nested Rent-Seeking Contest," Public Choice, Springer, vol. 87(1-2), pages 177-84, April.
  9. Rick Harbaugh & Tilman Klumpp, 2005. "Early Round Upsets and Championship Blowouts," Economic Inquiry, Western Economic Association International, vol. 43(2), pages 316-329, April.
  10. 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.
  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, 1998. "Influence and the discretionary allocation of several prizes," European Journal of Political Economy, Elsevier, vol. 14(4), pages 605-625, November.
  13. Gradstein, Mark & Konrad, Kai A, 1999. "Orchestrating Rent Seeking Contests," Economic Journal, Royal Economic Society, vol. 109(458), pages 536-45, October.
  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. 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.
  16. 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).
  17. 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.
  18. 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. 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, 2013. "Contest design and heterogeneity," Munich Reprints in Economics 19571, University of Munich, Department of Economics.
  4. Maria Arbatskaya & Hugo M. Mialon, 2012. "Dynamic Multi-Activity Contests," Scandinavian Journal of Economics, Wiley Blackwell, vol. 114(2), pages 520-538, 06.
  5. 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.
  6. Aner Sela & Eyal Erez, 2013. "Dynamic contests with resource constraints," Social Choice and Welfare, Springer, vol. 41(4), pages 863-882, October.
  7. 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.
  8. 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).
  9. Sheremeta, Roman, 2009. "Contest Design: An Experimental Investigation," MPRA Paper 52101, University Library of Munich, Germany.
  10. Sheremeta, Roman, 2009. "Essays on Experimental Investigation of Lottery Contests," MPRA Paper 49888, University Library of Munich, Germany.
  11. 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.
  12. 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).
  13. Hirata, Daisuke, 2014. "A model of a two-stage all-pay auction," Mathematical Social Sciences, Elsevier, vol. 68(C), pages 5-13.
  14. Kai Konrad & Dan Kovenock, 2012. "Introduction," Economic Theory, Springer, vol. 51(2), pages 241-245, October.
  15. 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.

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