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The optimal prize structure of symmetric Tullock contests

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  • Schweinzer, Paul
  • Segev, Ella

Abstract

We show that the optimal prize structure of symmetric n-player Tullock tournaments assigns the entire prize pool to the winner, provided that a symmetric pure strategy equilibrium exists. If such an equilibrium fails to exist under the winner-take-all structure, we construct the optimal prize structure which improves existence conditions by dampening efforts. If no such optimal equilibrium exists, no symmetric pure strategy equilibrium induces positive efforts.

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Bibliographic Info

Paper provided by Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich in its series Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems with number 250.

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Date of creation: Nov 2008
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Handle: RePEc:trf:wpaper:250

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Keywords: Tournaments; Incentive structures; Rent seeking;

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References

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  1. Richard Cornes & Roger Hartley, 2002. "Asymmetric Contests with General Technologies," Keele Economics Research Papers KERP 2002/22, Centre for Economic Research, Keele University.
  2. Gershkov, Alex & Perry, Motty, 2009. "Tournaments with midterm reviews," Games and Economic Behavior, Elsevier, vol. 66(1), pages 162-190, May.
  3. Hao Jia, 2008. "A stochastic derivation of the ratio form of contest success functions," Public Choice, Springer, vol. 135(3), pages 125-130, June.
  4. Stergios Skaperdas, 1996. "Contest success functions (*)," Economic Theory, Springer, vol. 7(2), pages 283-290.
  5. Fu, Qiang & Lu, Jingfeng, 2009. "The beauty of "bigness": On optimal design of multi-winner contests," Games and Economic Behavior, Elsevier, vol. 66(1), pages 146-161, May.
  6. 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.
  7. 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.
  8. Alcalde, José & Dahm, Matthias, 2010. "Rent seeking and rent dissipation: A neutrality result," Journal of Public Economics, Elsevier, vol. 94(1-2), pages 1-7, February.
  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. Ron Siegel, 2009. "All-Pay Contests," Econometrica, Econometric Society, vol. 77(1), pages 71-92, 01.
  11. Clark, Derek J & Riis, Christian, 1996. " A Multi-winner Nested Rent-Seeking Contest," Public Choice, Springer, vol. 87(1-2), pages 177-84, April.
  12. 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.
  13. Szymanski, Stefan & Valletti, Tommaso M., 2005. "Incentive effects of second prizes," European Journal of Political Economy, Elsevier, vol. 21(2), pages 467-481, June.
  14. 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.
  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. 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.
  17. Szidarovszky, Ferenc & Okuguchi, Koji, 1997. "On the Existence and Uniqueness of Pure Nash Equilibrium in Rent-Seeking Games," Games and Economic Behavior, Elsevier, vol. 18(1), pages 135-140, January.
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Citations

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Cited by:
  1. Giebe, Thomas, 2010. "Innovation Contests with Entry Auction," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 307, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
  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. Fu, Qiang & Lu, Jingfeng & Wang, Zhewei, 2014. "“Reverse” nested lottery contests," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 128-140.
  4. Megidish, Reut & Sela, Aner, 2009. "Allocation of Prizes in Contests with Participation Constraints," CEPR Discussion Papers 7580, C.E.P.R. Discussion Papers.
  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. Olivier Bos & Béatrice Roussillon & Paul Schweinzer, 2013. "Agreeing on Efficient Emissions Reduction," CESifo Working Paper Series 4345, CESifo Group Munich.
  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. Thomas Giebe & Paul Schweinzer, 2013. "Consuming your Way to Efficiency: Public Goods Provision through Non-Distortionary Tax Lotteries," CESifo Working Paper Series 4228, CESifo Group Munich.
  9. Christian Ewerhart, 2014. "Mixed equilibria in Tullock contests," ECON - Working Papers 143, Department of Economics - University of Zurich.
  10. Jingfeng Lu & Zhewei Wang, 2014. "Axiomatizing Multi-Prize Contests: A Perspective from Complete Ranking of Players," SDU Working Papers 2014-02, School of Economics, Shandong University.

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