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A nested contest: Tullock meets the All-Pay Auction

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  • Amegashie, J. Atsu

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.

Suggested Citation

  • Amegashie, J. Atsu, 2012. "A nested contest: Tullock meets the All-Pay Auction," MPRA Paper 41654, University Library of Munich, Germany, revised 03 Sep 2012.
    • Handle: RePEc:pra:mprapa:41654
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    References listed on IDEAS

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    1. J. Atsu Amegashie, 2009. "American Idol: should it be a singing contest or a popularity contest?," Journal of Cultural Economics, Springer;The Association for Cultural Economics International, vol. 33(4), pages 265-277, November.
    2. José Alcalde & Matthias Dahm, 2007. "Tullock and Hirshleifer: a meeting of the minds," Review of Economic Design, Springer;Society for Economic Design, vol. 11(2), pages 101-124, September.
    3. Franke, Jörg & Kanzow, Christian & Leininger, Wolfgang & Schwartz, Alexandra, 2014. "Lottery versus all-pay auction contests: A revenue dominance theorem," Games and Economic Behavior, Elsevier, vol. 83(C), pages 116-126.
    4. Ron Siegel, 2009. "All-Pay Contests," Econometrica, Econometric Society, vol. 77(1), pages 71-92, January.
    5. Michael R. Baye & Dan Kovenock & Casper G. Vries, 2008. "Rigging the lobbying process: An application of the all-pay auction," Springer Books, in: Roger D. Congleton & Kai A. Konrad & Arye L. Hillman (ed.), 40 Years of Research on Rent Seeking 2, pages 331-336, Springer.
    6. Amegashie, J Atsu, 2002. "Committees and Rent-Seeking Effort under Probabilistic Voting," Public Choice, Springer, vol. 112(3-4), pages 345-350, September.
    7. 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.
    8. Baye, Michael R & Kovenock, Dan & de Vries, Casper G, 1994. "The Solution to the Tullock Rent-Seeking Game When R Is Greater Than 2: Mixed-Strategy Equilibria and Mean Dissipation Rates," Public Choice, Springer, vol. 81(3-4), pages 363-380, December.
    9. Chowdhury, Subhasish M. & Sheremeta, Roman M., 2011. "Multiple equilibria in Tullock contests," Economics Letters, Elsevier, vol. 112(2), pages 216-219, August.
    10. 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.
    11. 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.
    12. Clark, D.J. & Riis, C., 1996. "On the Win Probability in Rent-Seeking Gemes," Memorandum 1996_005, Oslo University, Department of Economics.
    13. Michael R. Baye & Dan Kovenock & Casper G. Vries, 1996. "The all-pay auction with complete information," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 209-223, Springer.
    14. Epstein, Gil S. & Mealem, Yosef & Nitzan, Shmuel, 2011. "Political culture and discrimination in contests," Journal of Public Economics, Elsevier, vol. 95(1), pages 88-93.
    15. Arye L. Hillman & John G. Riley, 1989. "Politically Contestable Rents And Transfers," Economics and Politics, Wiley Blackwell, vol. 1(1), pages 17-39, 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," Papers 10-93-9, Pennsylvania State - Department of Economics.
    17. 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).
    18. Konrad, Kai A., 2009. "Strategy and Dynamics in Contests," OUP Catalogue, Oxford University Press, number 9780199549603.
    19. Fang, Hanming, 2002. "Lottery versus All-Pay Auction Models of Lobbying," Public Choice, Springer, vol. 112(3-4), pages 351-371, September.
    20. Hao Jia & Stergios Skaperdas, 2011. "Technologies of Conflict," Working Papers 101111, University of California-Irvine, Department of Economics.
    21. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(1), pages 1-26.
    22. Luis Corchón & Matthias Dahm, 2010. "Foundations for contest success functions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 43(1), pages 81-98, April.
    23. Roger D. Congleton, 1984. "Commitees and rent-seeking effort," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 279-291, Springer.
    24. Nitzan, Shmuel, 1994. "Modelling rent-seeking contests," European Journal of Political Economy, Elsevier, vol. 10(1), pages 41-60, May.
    25. 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.
    26. Hao Jia, 2008. "A stochastic derivation of the ratio form of contest success functions," Public Choice, Springer, vol. 135(3), pages 125-130, June.
    27. 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.
    28. Nti, Kofi O, 1999. "Rent-Seeking with Asymmetric Valuations," Public Choice, Springer, vol. 98(3-4), pages 415-430, March.
    29. 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.
    30. 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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    Cited by:

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    3. Xiaotie Deng & Yotam Gafni & Ron Lavi & Tao Lin & Hongyi Ling, 2021. "From Monopoly to Competition: Optimal Contests Prevail," Papers 2107.13363, arXiv.org.
    4. Ewerhart, Christian, 2017. "Contests with small noise and the robustness of the all-pay auction," Games and Economic Behavior, Elsevier, vol. 105(C), pages 195-211.

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    More about this item

    Keywords

    all-pay auction; discontinuous games; mixed strategy; pure strategy; Tullock contest;
    All these keywords.

    JEL classification:

    • B21 - Schools of Economic Thought and Methodology - - History of Economic Thought since 1925 - - - Microeconomics
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

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