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Asymmetric all-pay contests with heterogeneous prizes

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  • Xiao, Jun

Abstract

This paper studies complete-information, all-pay contests with asymmetric players competing for 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. The players are asymmetric as they incur different scoring costs, and they are assumed to have ordered marginal costs. The prize sequence is assumed to be either geometric or quadratic. We show that each such contest has a unique Nash equilibrium, and we exhibit an algorithm that constructs the equilibrium. Then, we apply the results to study the issue of tracking in schools and the optimality of winner-take-all contests.

Suggested Citation

  • Xiao, Jun, 2016. "Asymmetric all-pay contests with heterogeneous prizes," Journal of Economic Theory, Elsevier, vol. 163(C), pages 178-221.
    • Handle: RePEc:eee:jetheo:v:163:y:2016:i:c:p:178-221
    DOI: 10.1016/j.jet.2015.12.006
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    References listed on IDEAS

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    1. Benny Moldovanu & Aner Sela, 2001. "The Optimal Allocation of Prizes in Contests," American Economic Review, American Economic Association, vol. 91(3), pages 542-558, June.
    2. Benny Moldovanu & Aner Sela, 2008. "The Optimal Allocation of Prizes in Contests," Springer Books, in: Roger D. Congleton & Arye L. Hillman & Kai A. Konrad (ed.), 40 Years of Research on Rent Seeking 1, pages 615-631, Springer.
    3. 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.
    4. Esther Duflo & Pascaline Dupas & Michael Kremer, 2011. "Peer Effects, Teacher Incentives, and the Impact of Tracking: Evidence from a Randomized Evaluation in Kenya," American Economic Review, American Economic Association, vol. 101(5), pages 1739-1774, August.
    5. Ron Siegel, 2009. "All-Pay Contests," Econometrica, Econometric Society, vol. 77(1), pages 71-92, January.
    6. Szymanski, Stefan & Valletti, Tommaso M., 2005. "Incentive effects of second prizes," European Journal of Political Economy, Elsevier, vol. 21(2), pages 467-481, June.
    7. Parreiras, Sérgio O. & Rubinchik, Anna, 2010. "Contests with three or more heterogeneous agents," Games and Economic Behavior, Elsevier, vol. 68(2), pages 703-715, March.
    8. Ron Siegel, 2010. "Asymmetric Contests with Conditional Investments," American Economic Review, American Economic Association, vol. 100(5), pages 2230-2260, December.
    9. Jeremy Bulow & Jonathan Levin, 2006. "Matching and Price Competition," American Economic Review, American Economic Association, vol. 96(3), pages 652-668, June.
    10. 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.
    11. 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.
    12. Cohen, Chen & Sela, Aner, 2008. "Allocation of prizes in asymmetric all-pay auctions," European Journal of Political Economy, Elsevier, vol. 24(1), pages 123-132, March.
    13. Konrad, Kai A., 2009. "Strategy and Dynamics in Contests," OUP Catalogue, Oxford University Press, number 9780199549603.
    14. 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.
    15. Edward P. Lazear, 2001. "Educational Production," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 116(3), pages 777-803.
    16. 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.
    17. Clark, Derek J & Riis, Christian, 1998. "Competition over More Than One Prize," American Economic Review, American Economic Association, vol. 88(1), pages 276-289, March.
    Full references (including those not matched with items on IDEAS)

    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. Xiao, Jun, 2018. "All-pay contests with performance spillovers," Mathematical Social Sciences, Elsevier, vol. 92(C), pages 35-39.
    4. Thomas Giebe & Oliver Gürtler, 2024. "Player Strength and Effort in Contests," ECONtribute Discussion Papers Series 285, University of Bonn and University of Cologne, Germany.
    5. Olszewski, Wojciech & Siegel, Ron, 2020. "Performance-maximizing large contests," Theoretical Economics, Econometric Society, vol. 15(1), January.
    6. Yuanhao Zhang, 2023. "Contest in Multitasking: An Evidence from Chinese County Officials' Promotion Assessment," Papers 2302.08691, arXiv.org.
    7. Ghazala Azmat & Marc Möller, 2018. "The Distribution of Talent Across Contests," Economic Journal, Royal Economic Society, vol. 128(609), pages 471-509, March.
    8. 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.
    9. 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.
    10. 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.
    11. 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).
    12. Fu, Qiang & Wu, Zenan & Zhu, Yuxuan, 2022. "On equilibrium existence in generalized multi-prize nested lottery contests," Journal of Economic Theory, Elsevier, vol. 200(C).
    13. Xiao, Jun, 2023. "Ability grouping in contests," Journal of Mathematical Economics, Elsevier, vol. 104(C).
    14. Bas J. Dietzenbacher & Aleksei Y. Kondratev, 2023. "Fair and Consistent Prize Allocation in Competitions," Management Science, INFORMS, vol. 69(6), pages 3319-3339, June.
    15. Chen Cohen & Ishay Rabi & Aner Sela, 2022. "Assortative Matching by Lottery Contests," Games, MDPI, vol. 13(5), pages 1-20, September.
    16. Cohen, Chen & Lagziel, David & Levi, Ofer & Sela, Aner, 2023. "The role of the second prize in all-pay auctions with two heterogeneous prizes," Journal of Mathematical Economics, Elsevier, vol. 105(C).
    17. 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.
    18. Dahm, Matthias, 2018. "Semi-targeted all-pay auctions: A partial exclusion principle," International Journal of Industrial Organization, Elsevier, vol. 61(C), pages 256-282.
    19. Fu, Qiang & Wu, Zenan & Zhu, Yuxuan, 2023. "On equilibrium uniqueness in generalized multi-prize nested lottery contests," Games and Economic Behavior, Elsevier, vol. 139(C), pages 180-199.
    20. repec:hal:spmain:info:hdl:2441/2ldopuhqfp8e7oriqpulud8k5o is not listed on IDEAS
    21. Ghazala Azmat & Marc Möller, 2018. "The Distribution of Talent Across Contests," SciencePo Working papers hal-03263984, HAL.
    22. 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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    More about this item

    Keywords

    All-pay; Asymmetric; Contest; Heterogeneous;
    All these keywords.

    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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