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Asymmetric All-Pay Contests with Heterogeneous

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  • Jun Xiao

Abstract

This paper studies complete-information, all-pay contests with asymmetric players competing for multiple heterogeneous prizes. In these contests, each player chooses a performance level or score. The first prize is awarded to the player with the highest score,the second,less valuable prize to the player with the second highest score, etc. Players are asymmetric in that they incur di¤erent costs of score. The players are assumed to have ordered marginal costs, and the prize sequence is assumed to be either quadratic or geometric. I show that each such contest has a unique Nash equilibrium and exhibit an algorithm that constructs the equilibrium. I then apply the main result to study: (a) the issue of tracking students in schools, (b) the incentive e¤ects of superstars,and (c)the optimality of winner-take-all contests.

Suggested Citation

  • Jun Xiao, 2012. "Asymmetric All-Pay Contests with Heterogeneous," Department of Economics - Working Papers Series 1151, The University of Melbourne.
    • Handle: RePEc:mlb:wpaper:1151
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    File URL: http://fbe.unimelb.edu.au/__data/assets/pdf_file/0006/784311/1151.pdf
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    References listed on IDEAS

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    1. Jennifer Brown, 2011. "Quitters Never Win: The (Adverse) Incentive Effects of Competing with Superstars," Journal of Political Economy, University of Chicago Press, vol. 119(5), pages 982-1013.
    2. Konrad, Kai A., 2009. "Strategy and Dynamics in Contests," OUP Catalogue, Oxford University Press, number 9780199549603, Decembrie.
    3. 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.
    4. Jeremy Bulow & Jonathan Levin, 2006. "Matching and Price Competition," American Economic Review, American Economic Association, vol. 96(3), pages 652-668, June.
    5. Lizzeri, Alessandro & Persico, Nicola, 2000. "Uniqueness and Existence of Equilibrium in Auctions with a Reserve Price," Games and Economic Behavior, Elsevier, vol. 30(1), pages 83-114, January.
    6. Barut, Yasar & Kovenock, Dan, 1998. "The symmetric multiple prize all-pay auction with complete information," European Journal of Political Economy, Elsevier, vol. 14(4), pages 627-644, November.
    7. Amann, Erwin & Leininger, Wolfgang, 1996. "Asymmetric All-Pay Auctions with Incomplete Information: The Two-Player Case," Games and Economic Behavior, Elsevier, vol. 14(1), pages 1-18, May.
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    Citations

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    Cited by:

    1. Letina, Igor & Liu, Shuo & Netzer, Nick, 2023. "Optimal contest design: Tuning the heat," Journal of Economic Theory, Elsevier, vol. 213(C).
    2. Xiao, Jun, 2018. "Equilibrium analysis of the all-pay contest with two nonidentical prizes: Complete results," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 21-34.
    3. Olszewski, Wojciech & Siegel, Ron, 2020. "Performance-maximizing large contests," Theoretical Economics, Econometric Society, vol. 15(1), January.
    4. Siegel, Ron, 2014. "Asymmetric all-pay auctions with interdependent valuations," Journal of Economic Theory, Elsevier, vol. 153(C), pages 684-702.
    5. Ghazala Azmat & Marc Möller, 2018. "The Distribution of Talent Across Contests," Economic Journal, Royal Economic Society, vol. 128(609), pages 471-509, March.
    6. 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.
    7. Matthias Dahm, 2017. "All-Pay Auctions with Extra Prize: A Partial Exclusion Principle," Discussion Papers 2017-01, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    8. Chen Cohen & David Lagziel & Ofer Levi & Aner Sela, 2020. "All-Pay Auctions With Heterogeneous Prizes And Partially Asymmetric Players," Working Papers 2010, Ben-Gurion University of the Negev, Department of Economics.
    9. Mendel, Moritz & Pieroth, Ferdinand & Seel, Christian, 2021. "Your failure is my opportunity—Effects of elimination in contests," Journal of Mathematical Economics, Elsevier, vol. 95(C).
    10. Ghazala Azmat & Marc Möller, 2016. "The Distribution of Talent across Contests Feedback in Higher Education," Working Papers 789, Queen Mary University of London, School of Economics and Finance.
    11. Dahm, Matthias, 2018. "Semi-targeted all-pay auctions: A partial exclusion principle," International Journal of Industrial Organization, Elsevier, vol. 61(C), pages 256-282.
    12. Julio González-Díaz & Ron Siegel, 2013. "Matching and price competition: beyond symmetric linear costs," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(4), pages 835-844, November.
    13. repec:hal:spmain:info:hdl:2441/2ldopuhqfp8e7oriqpulud8k5o is not listed on IDEAS
    14. Ghazala Azmat & Marc Möller, 2018. "The Distribution of Talent Across Contests," Economic Journal, Royal Economic Society, vol. 128(609), pages 471-509, March.

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    Keywords

    all-pay; contest; asymmetric; heterogeneous;
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