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A Nested Contest: Tullock Meets the All-pay Auction

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  • J. Atsu Amegashie

Abstract

I present a two-player nested contest which is a convex combination of two widely studied contests: the Tullock (lottery) contest and the all-pay auction. A Nash equilibrium exists for all parameters of the nested contest. If and only if the contest is sufficiently asymmetric, then there is an equilibrium in pure strategies. In this equilibrium, individual and aggregate efforts are lower relative to the efforts in a Tullock contest. This leads to the surprising result that if aggregate efforts in the all-pay auction are higher than the aggregate efforts in the Tullock contest, then aggregate efforts in the nested contest may not lie between aggregate efforts in the all-pay auction and aggregate efforts in the Tullock contest. When the contest is symmetric or asymmetric, I find a mixed-strategy equilibrium and describe some properties of the equilibrium distribution function; I also find the equilibrium payoffs and expected bids. When the weight on the all-pay auction component of this nested contest lies in an intermediate range, then there exist multiple non-payoff-equivalent equilibria such that there is an all-pay auction equilibrium as defined in Alcade and Dahm (2010) and another equilibrium which is not an all-pay auction equilibrium; these equilibria cannot be ranked using the Pareto criterion. If the goal of a contest-designer is to reduce aggregate effort (i.e., wasteful rent-seeking efforts), then this nested contest may be better than both the Tullock contest and the all-pay auction.

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Bibliographic Info

Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 3976.

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Date of creation: 2012
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Handle: RePEc:ces:ceswps:_3976

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Keywords: all-pay auction; discontinuous games; mixed strategy; pure strategy; Tullock contest;

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References

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  1. Arye L. Hillman & John G. Riley, 1987. "Politically Contestable Rents and Transfers," UCLA Economics Working Papers 452, UCLA Department of Economics.
  2. 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.
  3. Corchón, Luis C. & Dahm, Matthias, 2008. "Foundations for contest success functions," Working Papers 2072/9493, Universitat Rovira i Virgili, Department of Economics.
  4. Amegashie, J. Atsu, 2007. "American Idol: Should it be a Singing Contest or a Popularity Contest?," MPRA Paper 6465, University Library of Munich, Germany.
  5. 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.
  6. Franke, Jörg & Kanzow, Christian & Leininger, Wolfgang & Schwartz, Alexandra, 2013. "Lottery versus All-Pay Auction Contests: A Revenue Dominance Theorem," Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 79998, Verein für Socialpolitik / German Economic Association.
  7. Gil Epstein & Shmuel Nitzan, 2006. "Reduced prizes and increased effort in contests," Social Choice and Welfare, Springer, vol. 26(3), pages 447-453, June.
  8. Dasgupta, Partha & Maskin, Eric, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," Review of Economic Studies, Wiley Blackwell, vol. 53(1), pages 1-26, January.
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  10. Baye, M.R. & Kovenock, D. & De Vries, C.G., 1991. "The All-Pay Auction With Complete Information," Purdue University Economics Working Papers 1007, Purdue University, Department of Economics.
  11. Chowdhury, Subhasish M. & Sheremeta, Roman M., 2011. "Multiple equilibria in Tullock contests," Economics Letters, Elsevier, vol. 112(2), pages 216-219, August.
  12. Jia, Hao & Skaperdas, Stergios & Vaidya, Samarth, 2013. "Contest functions: Theoretical foundations and issues in estimation," International Journal of Industrial Organization, Elsevier, vol. 31(3), pages 211-222.
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  14. Alcalde, José & Dahm, Matthias, 2008. "All-pay auction equilibria in contests," Working Papers 2072/5368, Universitat Rovira i Virgili, Department of Economics.
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  16. José Alcalde & Matthias Dahm, 2007. "Tullock And Hirshleifer: A Meeting Of The Minds," Working Papers. Serie AD 2007-13, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  17. 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.
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  19. Amegashie, J Atsu, 2002. " Committees and Rent-Seeking Effort under Probabilistic Voting," Public Choice, Springer, vol. 112(3-4), pages 345-50, September.
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  21. 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.
  22. Clark, D.J. & Riis, C., 1996. "On the Win Probability in Rent-Seeking Gemes," Memorandum 05/1996, Oslo University, Department of Economics.
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Cited by:
  1. Christian Ewerhart, 2014. "Mixed equilibria in Tullock contests," ECON - Working Papers 143, Department of Economics - University of Zurich.

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