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A Nested Contest: Tullock Meets the All-Pay Auction

  • J. Atsu Amegashie

    ()

    (Department of Economics, University of Guelph.)

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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Paper provided by University of Guelph, Department of Economics and Finance in its series Working Papers with number 1211.

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Length: 31 pages
Date of creation: 2012
Date of revision:
Handle: RePEc:gue:guelph:2012-11
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  1. Chowdhury, Subhasish & Sheremeta, Roman, 2011. "Multiple Equilibria in Tullock Contests," MPRA Paper 52104, University Library of Munich, Germany.
  2. Gil Epstein & Igal Milchtaich & Shmuel Nitzan & Mordechai Schwarz, 2007. "Ambiguous political power and contest efforts," Public Choice, Springer, vol. 132(1), pages 113-123, July.
  3. Baye, M.R. & Kovenock, D. & De Varies, C.G., 1990. "The All-Pay Auction With Complete Information," Papers 9051, Tilburg - Center for Economic Research.
  4. 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.
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  6. J. Atsu Amegashie, 2009. "American Idol: should it be a singing contest or a popularity contest?," Journal of Cultural Economics, Springer, vol. 33(4), pages 265-277, November.
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  8. José Alcalde & Matthias Dahm, 2007. "All-Pay Auction Equilibria In Contests," Working Papers. Serie AD 2007-27, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  9. Leonid Polishchuk & Alexander Tonis, 2013. "Endogenous contest success functions: a mechanism design approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(1), pages 271-297, January.
  10. 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.
  11. 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.
  12. 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).
  13. Hao Jia & Stergios Skaperdas & Samarth Vaidya, 2012. "Contest Functions: Theoretical Foundations and Issues in Estimation," Working Papers 111214, University of California-Irvine, Department of Economics.
  14. Corchón, Luis C. & Dahm, Matthias, 2007. "Foundations for contest success functions," UC3M Working papers. Economics we070401, Universidad Carlos III de Madrid. Departamento de Economía.
  15. Arye L. Hillman & John G. Riley, 1987. "Politically Contestable Rents and Transfers," UCLA Economics Working Papers 452, UCLA Department of Economics.
  16. Clark, D.J. & Riis, C., 1996. "On the Win Probability in Rent-Seeking Gemes," Memorandum 05/1996, Oslo University, Department of Economics.
  17. Amegashie, J Atsu, 2002. "Committees and Rent-Seeking Effort under Probabilistic Voting," Public Choice, Springer, vol. 112(3-4), pages 345-50, September.
  18. 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.
  19. Che, Yeon-Koo & Gale, Ian, 2000. "Difference-Form Contests and the Robustness of All-Pay Auctions," Games and Economic Behavior, Elsevier, vol. 30(1), pages 22-43, January.
  20. Gil Epstein & Shmuel Nitzan, 2006. "Reduced prizes and increased effort in contests," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 26(3), pages 447-453, June.
  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. Nti, Kofi O, 1999. "Rent-Seeking with Asymmetric Valuations," Public Choice, Springer, vol. 98(3-4), pages 415-30, March.
  23. Hao Jia, 2008. "A stochastic derivation of the ratio form of contest success functions," Public Choice, Springer, vol. 135(3), pages 125-130, June.
  24. Nitzan, Shmuel, 1994. "Modelling rent-seeking contests," European Journal of Political Economy, Elsevier, vol. 10(1), pages 41-60, May.
  25. Gil Epstein & Shmuel Nitzan, 2006. "The Politics of Randomness," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(2), pages 423-433, October.
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