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A Nested Contest: Tullock Meets the All-Pay Auction

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  • J. Atsu Amegashie

    ()
    (Department of Economics, University of Guelph.)

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

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References

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  1. 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," Papers 10-93-9, Pennsylvania State - Department of Economics.
  2. Corchón, Luis C. & Dahm, Matthias, 2008. "Foundations for contest success functions," Working Papers 2072/9493, Universitat Rovira i Virgili, Department of Economics.
  3. Kovenock, D. & de Vries, C.G., 1995. "The All-Pay Auction with Complete Information," UFAE and IAE Working Papers 311.95, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  4. 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).
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  6. 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.
  7. José Alcalde & Matthias Dahm, 2007. "Tullock and Hirshleifer: a meeting of the minds," Review of Economic Design, Springer, vol. 11(2), pages 101-124, September.
  8. Nti, Kofi O, 1999. " Rent-Seeking with Asymmetric Valuations," Public Choice, Springer, vol. 98(3-4), pages 415-30, March.
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  10. Che,Y.K. & Gale,I., 1998. "Difference-form contests and the robustness of all-pay auctions," Working papers 6, Wisconsin Madison - Social Systems.
  11. Subhashish Modak Chowdhury & Roman M. Sheremeta, 2010. "Multiple equilibria in Tullock contests," Working Paper series, University of East Anglia, Centre for Behavioural and Experimental Social Science (CBESS) 10-12, School of Economics, University of East Anglia, Norwich, UK..
  12. 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.
  13. 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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  15. Gil Epstein & Shmuel Nitzan, 2006. "The Politics of Randomness," Social Choice and Welfare, Springer, vol. 27(2), pages 423-433, October.
  16. J. Atsu Amegashie, 2007. "American Idol: Should it be a Singing Contest or a Popularity Contest?," Working Papers 0708, University of Guelph, Department of Economics and Finance.
  17. Ron Siegel, 2009. "All-Pay Contests," Econometrica, Econometric Society, vol. 77(1), pages 71-92, 01.
  18. Nitzan, Shmuel, 1994. "Modelling rent-seeking contests," European Journal of Political Economy, Elsevier, vol. 10(1), pages 41-60, May.
  19. Amegashie, J Atsu, 2002. " Committees and Rent-Seeking Effort under Probabilistic Voting," Public Choice, Springer, vol. 112(3-4), pages 345-50, September.
  20. 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.
  21. Jörg Franke & Christian Kanzow & Wolfgang Leininger & Alexandra Schwartz, 2012. "Lottery versus All-Pay Auction Contests – A Revenue Dominance Theorem," Ruhr Economic Papers 0315, Rheinisch-Westfälisches Institut für Wirtschaftsforschung, Ruhr-Universität Bochum, Universität Dortmund, Universität Duisburg-Essen.
  22. Hao Jia, 2008. "A stochastic derivation of the ratio form of contest success functions," Public Choice, Springer, vol. 135(3), pages 125-130, June.
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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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