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Mixed equilibria in Tullock contests

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  • Christian Ewerhart

Abstract

Any symmetric mixed-strategy equilibrium in a Tullock contest with intermediate values of the decisiveness parameter (“ $$2>R>\infty $$ 2 > R > ∞ ”) has countably infinitely many mass points. All probability weight is concentrated on those mass points, which have the zero bid as their sole point of accumulation. With contestants randomizing over a non-convex set, there is a cost of being “halfhearted,” which is absent from both the lottery contest and the all-pay auction. Numerical bid distributions are generally negatively skewed and exhibit, for some parameter values, a higher probability of ex-post overdissipation than the all-pay auction. Copyright The Author(s) 2015

Suggested Citation

  • Christian Ewerhart, 2015. "Mixed equilibria in Tullock contests," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(1), pages 59-71, September.
  • Handle: RePEc:spr:joecth:v:60:y:2015:i:1:p:59-71
    DOI: 10.1007/s00199-014-0835-x
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    1. Yang, Chun-Lei, 1994. "A simple extension of the Dasgupta-Maskin existence theorem for discontinuous games with an application to the theory of rent-seeking," Economics Letters, Elsevier, vol. 45(2), pages 181-183, June.
    2. Christian Ewerhart, 2014. "Elastic contests and the robustness of the all-pay auctions," ECON - Working Papers 155, Department of Economics - University of Zurich.
    3. Johannes Münster, 2007. "Rents, dissipation and lost treasures: Comment," Public Choice, Springer, vol. 130(3), pages 329-335, March.
    4. 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.
    5. Paul Schweinzer & Ella Segev, 2012. "The optimal prize structure of symmetric Tullock contests," Public Choice, Springer, vol. 153(1), pages 69-82, October.
    6. Giuseppe Dari-Mattiacci & Francesco Parisi, 2005. "Rents, dissipation and lost treasures: Rethinking Tullock's paradox," Public Choice, Springer, vol. 124(3), pages 411-422, September.
    7. Nti, Kofi O, 1999. "Rent-Seeking with Asymmetric Valuations," Public Choice, Springer, vol. 98(3-4), pages 415-430, March.
    8. Dan Kovenock & Michael R. Baye & Casper G. de Vries, 1996. "The all-pay auction with complete information (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 291-305.
    9. Konrad, Kai A. & Kovenock, Dan, 2009. "Multi-battle contests," Games and Economic Behavior, Elsevier, vol. 66(1), pages 256-274, May.
    10. Perez-Castrillo, J David & Verdier, Thierry, 1992. "A General Analysis of Rent-Seeking Games," Public Choice, Springer, vol. 73(3), pages 335-350, April.
    11. Arye Hillman & Dov Samet, 1987. "Dissipation of contestable rents by small numbers of contenders," Public Choice, Springer, vol. 54(1), pages 63-82, January.
    12. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," Review of Economic Studies, Oxford University Press, vol. 53(1), pages 1-26.
    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. 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.
    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. J. Atsu Amegashie, 2012. "A Nested Contest: Tullock Meets the All-pay Auction," CESifo Working Paper Series 3976, CESifo.
    17. Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, II: Applications," Review of Economic Studies, Oxford University Press, vol. 53(1), pages 27-41.
    18. Baye, Michael R & Kovenock, Dan & de Vries, Casper G, 1999. "The Incidence of Overdissipation in Rent-Seeking Contests," Public Choice, Springer, vol. 99(3-4), pages 439-454, June.
    19. Baye, M.R. & Kovenock, D., 1993. "The Solution to the Tullock Rent-Seeking Game When R > 2: Mixed Strategy Equilibria and Mean Dissipation Rates," Papers 9368, Tilburg - Center for Economic Research.
    20. Jörg Franke & Christian Kanzow & Wolfgang Leininger & Alexandra Schwartz, 2013. "Effort maximization in asymmetric contest games with heterogeneous contestants," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 52(2), pages 589-630, March.
    21. 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:

    1. Heijnen, Pim & Schoonbeek, Lambert, 2019. "Rent-seeking with uncertain discriminatory power," European Journal of Political Economy, Elsevier, vol. 56(C), pages 103-114.
    2. Ewerhart, Christian, 2017. "Revenue ranking of optimally biased contests: The case of two players," Economics Letters, Elsevier, vol. 157(C), pages 167-170.
    3. Arye Hillman & Ngo Van Long, 2017. "The social cost of contestable benefits," CIRANO Working Papers 2017s-11, CIRANO.
    4. Drugov, Mikhail & Ryvkin, Dmitry, 2020. "How noise affects effort in tournaments," Journal of Economic Theory, Elsevier, vol. 188(C).
    5. David K Levine & Andrea Mattozzi, 2021. "Success in Contests," Levine's Working Paper Archive 786969000000001563, David K. Levine.
    6. Balart, Pau & Chowdhury, Subhasish M. & Troumpounis, Orestis, 2017. "Linking individual and collective contests through noise level and sharing rules," Economics Letters, Elsevier, vol. 155(C), pages 126-130.
    7. Arye L. Hillman & Ngo Van Long, 2017. "Rent Seeking: The Social Cost of Contestable Benefits," CESifo Working Paper Series 6462, CESifo.
    8. Christian Ewerhart, 2014. "Elastic contests and the robustness of the all-pay auctions," ECON - Working Papers 155, Department of Economics - University of Zurich.
    9. Martin Gregor, 2016. "Tullock's Puzzle in Pay-and-Play Lobbying," Economics and Politics, Wiley Blackwell, vol. 28(3), pages 368-389, November.
    10. 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.
    11. Segev, Ella, 2020. "Crowdsourcing contests," European Journal of Operational Research, Elsevier, vol. 281(2), pages 241-255.
    12. Paul Pecorino, 2020. "Bridge burning and escape routes," Public Choice, Springer, vol. 184(3), pages 399-414, September.
    13. Doron Klunover & John Morgan, 2018. "A note on contests with a constrained choice set of effort," Papers 1809.04436, arXiv.org, revised Sep 2020.
    14. Osório António, 2018. "Conflict and Competition over Multi-Issues," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 18(2), pages 1-17, July.
    15. Christian Ewerhart & Guang-Zhen Sun, 2020. "The n-player Hirshleifer contest," ECON - Working Papers 361, Department of Economics - University of Zurich.
    16. Osório, António (António Miguel), 2018. "Conflict and Competition over Multi-Issues," Working Papers 2072/306550, Universitat Rovira i Virgili, Department of Economics.
    17. Feng, Xin & Lu, Jingfeng, 2017. "Uniqueness of equilibrium in two-player asymmetric Tullock contests with intermediate discriminatory power," Economics Letters, Elsevier, vol. 159(C), pages 61-64.
    18. Yosef Mealem & Shmuel Nitzan, 2016. "Discrimination in contests: a survey," Review of Economic Design, Springer;Society for Economic Design, vol. 20(2), pages 145-172, June.
    19. Alexander Matros & David Michael Rietzke, 2017. "Contests on Networks," Working Papers 156630581, Lancaster University Management School, Economics Department.
    20. Ewerhart, Christian, 2016. "An envelope approach to tournament design," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 1-9.
    21. Ben J. Heijdra & Pim Heijnen, 2021. "Efficiency and Equity: A General Equilibrium Analysis of Rent-Seeking," CESifo Working Paper Series 9375, CESifo.
    22. Christian Ewerhart, 2015. "Contest success functions: the common-pool perspective," ECON - Working Papers 195, Department of Economics - University of Zurich.

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    More about this item

    Keywords

    Tullock contest; Mixed-strategy Nash equilibrium; Analytical functions; C72; D72; C16;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions

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