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Allocation of Prizes in Asymmetric All-Pay Auctions

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  • Sela, Aner
  • Cohen, Chen

Abstract

We study asymmetric all-pay auctions with multiple objects where players? values for the objects are common knowledge. The players have different values for the objects but they have the same ranking. The contest designer may award one prize including all the objects to the player with the highest bid, or, alternatively, they may allocate several prizes, each prize including one object such that the first prize is awarded to the player with the highest bid, the second prize to the player with the second-highest bid, and so on until all the objects are allocated. We analyse the distribution of effort in one-prize and multiple-prize contests and show that allocation of several prizes may be optimal for a contest designer who maximizes the total effort.

Suggested Citation

  • Sela, Aner & Cohen, Chen, 2005. "Allocation of Prizes in Asymmetric All-Pay Auctions," CEPR Discussion Papers 4951, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:4951
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    References listed on IDEAS

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    1. 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.
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    4. Moldovanu, Benny & Sela, Aner, 2006. "Contest architecture," Journal of Economic Theory, Elsevier, vol. 126(1), pages 70-96, January.
    5. Konrad, Kai A., 2006. "Silent interests and all-pay auctions," International Journal of Industrial Organization, Elsevier, vol. 24(4), pages 701-713, July.
    6. Arye Hillman & Dov Samet, 1987. "Dissipation of contestable rents by small numbers of contenders," Public Choice, Springer, vol. 54(1), pages 63-82, January.
    7. Arieh Gavious & Benny Moldovanu & Aner Sela, 2002. "Bid Costs and Endogenous Bid Caps," RAND Journal of Economics, The RAND Corporation, vol. 33(4), pages 709-722, Winter.
    8. Yeon-Koo Che & Ian L. Gale, 2008. "Caps on Political Lobbying," Springer Books, in: Roger D. Congleton & Kai A. Konrad & Arye L. Hillman (ed.), 40 Years of Research on Rent Seeking 2, pages 337-345, Springer.
    9. Szymanski, Stefan & Valletti, Tommaso, 2004. "First and Second Prizes in Imperfectly Discriminating Contests," CEPR Discussion Papers 4484, C.E.P.R. Discussion Papers.
    10. Arye L. Hillman & John G. Riley, 1989. "Politically Contestable Rents And Transfers," Economics and Politics, Wiley Blackwell, vol. 1(1), pages 17-39, March.
    11. 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.
    12. 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.
    13. Cohen, Chen & Sela, Aner, 2005. "Manipulations in contests," Economics Letters, Elsevier, vol. 86(1), pages 135-139, January.
    14. 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.
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    Citations

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    Cited by:

    1. Aner Sela, 2020. "Optimal allocations of prizes and punishments in Tullock contests," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(3), pages 749-771, September.
    2. Matros, Alexander, 2012. "Sad-Loser contests," Journal of Mathematical Economics, Elsevier, vol. 48(3), pages 155-162.
    3. 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.
    4. Kräkel, Matthias, 2012. "Competitive careers as a way to mediocracy," European Journal of Political Economy, Elsevier, vol. 28(1), pages 76-87.
    5. Aner Sela, 2012. "Sequential two-prize contests," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(2), pages 383-395, October.
    6. Ghazala Azmat & Marc Möller, 2018. "The Distribution of Talent Across Contests," Economic Journal, Royal Economic Society, vol. 128(609), pages 471-509, March.
    7. repec:elg:eechap:15325_3 is not listed on IDEAS
    8. Van Long, Ngo, 2013. "The theory of contests: A unified model and review of the literature," European Journal of Political Economy, Elsevier, vol. 32(C), pages 161-181.
    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. 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.
    11. Alex Krumer & Reut Megidish & Aner Sela, 2020. "The optimal design of round-robin tournaments with three players," Journal of Scheduling, Springer, vol. 23(3), pages 379-396, June.
    12. Subhasish M. Chowdhury & Patricia Esteve‐González & Anwesha Mukherjee, 2023. "Heterogeneity, leveling the playing field, and affirmative action in contests," Southern Economic Journal, John Wiley & Sons, vol. 89(3), pages 924-974, January.
    13. Lauber, Arne & March, Christoph & Sahm, Marco, 2023. "Optimal and fair prizing in sequential round-robin tournaments: Experimental evidence," Games and Economic Behavior, Elsevier, vol. 141(C), pages 30-51.
    14. 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.
    15. Dahm, Matthias, 2018. "Semi-targeted all-pay auctions: A partial exclusion principle," International Journal of Industrial Organization, Elsevier, vol. 61(C), pages 256-282.
    16. repec:hal:spmain:info:hdl:2441/2ldopuhqfp8e7oriqpulud8k5o is not listed on IDEAS
    17. Ghazala Azmat & Marc Möller, 2018. "The Distribution of Talent Across Contests," SciencePo Working papers hal-03263984, HAL.
    18. Ryvkin, Dmitry, 2010. "Contests with private costs: Beyond two players," European Journal of Political Economy, Elsevier, vol. 26(4), pages 558-567, December.
    19. Ghazala Azmat & Marc Möller, 2018. "The Distribution of Talent Across Contests," Economic Journal, Royal Economic Society, vol. 128(609), pages 471-509, March.
    20. Xiao, Jun, 2016. "Asymmetric all-pay contests with heterogeneous prizes," Journal of Economic Theory, Elsevier, vol. 163(C), pages 178-221.

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    More about this item

    Keywords

    Contests; Auctions;

    JEL classification:

    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

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