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Contests with Ties

Author

Listed:
  • Cohen Chen

    (Ben-Gurion University)

  • Sela Aner

    (Ben-Gurion University)

Abstract

We study two-player all-pay contests in which there is a positive probability of a tied outcome. We show that the players' efforts in equilibrium do not depend on the expected prize in the case of a tie given that this prize is smaller than the prize for winning. The implications of this result are twofold. First, in symmetric one-stage contests, the designer who wishes to maximize the expected total effort should not award a prize in the case of a tie which is larger than one-third of the prize for winning. Second, in multi-stage contests, the designer should not limit the number of stages (tie-breaks) but should allow the contest to continue until a winner is decided.

Suggested Citation

  • Cohen Chen & Sela Aner, 2007. "Contests with Ties," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 7(1), pages 1-18, December.
    • Handle: RePEc:bpj:bejtec:v:7:y:2007:i:1:n:43
    DOI: 10.2202/1935-1704.1398
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    References listed on IDEAS

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    Cited by:

    1. Philipp Ager & Leonardo Bursztyn & Hans-Joachim Voth, 2016. "Killer Incentives: Status Competition and Pilot Performance during World War II," NBER Working Papers 22992, National Bureau of Economic Research, Inc.
    2. Matthias Kräkel, 2014. "Optimal seedings in elimination tournaments revisited," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 2(1), pages 77-91, April.
    3. Han Feng & David Hobson, 2015. "Gambling in contests modelled with diffusions," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 38(1), pages 21-37, April.
    4. Alberto Vesperoni, 2016. "A contest success function for rankings," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(4), pages 905-937, December.
    5. Li, Bo & Wu, Zenan & Xing, Zeyu, 2023. "Optimally biased contests with draws," Economics Letters, Elsevier, vol. 226(C).
    6. Yizhaq Minchuk, 2022. "Winner‐pay contests with a no‐winner possibility," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 43(6), pages 1874-1879, September.
    7. Cohen, Chen & Levi, Ofer & Sela, Aner, 2019. "All-pay auctions with asymmetric effort constraints," Mathematical Social Sciences, Elsevier, vol. 97(C), pages 18-23.
    8. Alan Gelder & Dan Kovenock & Brian Roberson, 2022. "All-pay auctions with ties," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(4), pages 1183-1231, November.
    9. Luis C. Corchón & Marco Serena, 2016. "Properties of Contests," Working Papers tax-mpg-rps-2018-10, Max Planck Institute for Tax Law and Public Finance.
    10. Gil S. Epstein & Ira N. Gang, 2010. "A Political Economy of the Immigrant Assimilation: Internal Dynamics," Working Papers 2010-13, Bar-Ilan University, Department of Economics.
    11. Pradeep Dubey & John Geanakoplos, 2016. "Money and Status: How Best to Incentivize Work," Department of Economics Working Papers 16-02, Stony Brook University, Department of Economics.
    12. Oindrila Dey & Swapnendu Banerjee, 2014. "Status Incentives with Discrete Effort: A Note," Economics Bulletin, AccessEcon, vol. 34(2), pages 1205-1213.
    13. Maya Eden, 2006. "Optimal Ties in Contests," Discussion Paper Series dp430, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    14. Brownback, Andy, 2018. "A classroom experiment on effort allocation under relative grading," Economics of Education Review, Elsevier, vol. 62(C), pages 113-128.
    15. Lorens Imhof & Matthias Kräkel, 2016. "Ex post unbalanced tournaments," RAND Journal of Economics, RAND Corporation, vol. 47(1), pages 73-98, February.
    16. Marcin Dziubiński, 2013. "Non-symmetric discrete General Lotto games," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(4), pages 801-833, November.
    17. Gelder, Alan & Kovenock, Dan & Sheremeta, Roman, 2015. "Behavior in All-Pay Auctions with Ties," MPRA Paper 67517, University Library of Munich, Germany.
    18. HHironori Otsubo, 2012. "Contests with Incumbency Advantages: An Experiment Investigation of the Effect of Limits on Spending Behavior and Outcome," Jena Economics Research Papers 2012-020, Friedrich-Schiller-University Jena.
    19. Shelegia, Sandro & Wilson, Chris M., 2022. "Costly participation and default allocations in all-pay contests," MPRA Paper 115027, University Library of Munich, Germany.
    20. Aner Sela, 2023. "Resource allocations in the best-of-k ( $$k=2,3$$ k = 2 , 3 ) contests," Journal of Economics, Springer, vol. 139(3), pages 235-260, August.
    21. Lang, Matthias & Seel, Christian & Strack, Philipp, 2014. "Deadlines in stochastic contests," Journal of Mathematical Economics, Elsevier, vol. 52(C), pages 134-142.
    22. Li, Zheng, 2017. "Nash equilibria in all-pay auctions with discrete strategy space," Economics Discussion Papers 2017-22, Kiel Institute for the World Economy (IfW Kiel).
    23. Aner Sela, 2022. "Ineffective Prizes In Multi-Dimensional Contests," Working Papers 2205, Ben-Gurion University of the Negev, Department of Economics.

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    More about this item

    JEL classification:

    • 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

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