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Best-of-Three All-Pay Auctions

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  • Sela, Aner

Abstract

We study a three-stage all-pay auction with two players in which the first player to win two matches wins the best-of-three all-pay auction. The players have values of winning the contest and may have also values of losing, the latter depending on the stage in which the contest is decided. It is shown that without values of losing, if players are heterogenous (they have different values) the best-of-three all-pay auction is less competitive (the difference between the players' probabilities to win is larger) as well as less productive (the players' total expected effort is smaller) than the one-stage all-pay auction. If players are homogenous, however, the productivity and obviously the competitiveness of the best-of-three all-pay auction and the one-stage all-pay auction are identical. These results hold even if players have values of losing that do not depend on the stage in which the contest is decided. However, the best-of-three all-pay auction with different values of losing over the contest's stages may be more productive than the one-stage all-pay auction.

Suggested Citation

  • Sela, Aner, 2009. "Best-of-Three All-Pay Auctions," CEPR Discussion Papers 7224, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:7224
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    Cited by:

    1. Klein, Arnd Heinrich & Schmutzler, Armin, 2017. "Optimal effort incentives in dynamic tournaments," Games and Economic Behavior, Elsevier, vol. 103(C), pages 199-224.
    2. Todd R. Kaplan & David Wettstein, 2022. "Two-stage contests with preferences over style," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 74(4), pages 1141-1161, November.
    3. Alex Krumer & Reut Megidish & Aner Sela, 2017. "First-mover advantage in round-robin tournaments," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(3), pages 633-658, March.
    4. Aner Sela, 2021. "Resource Allocations In Multi-Stage Contests," Working Papers 2105, Ben-Gurion University of the Negev, Department of Economics.
    5. Kaplan, Todd R. & Zamir, Shmuel, 2015. "Advances in Auctions," Handbook of Game Theory with Economic Applications,, Elsevier.
    6. Aniruddha Bagchi & João Ricardo Faria & Timothy Mathews, 2019. "A model of a multilateral proxy war with spillovers," Public Choice, Springer, vol. 179(3), pages 229-248, June.
    7. Feng, Xin & Lu, Jingfeng, 2018. "How to split the pie: Optimal rewards in dynamic multi-battle competitions," Journal of Public Economics, Elsevier, vol. 160(C), pages 82-95.
    8. 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.
    9. Xiandeng Jiang, 2018. "Relative Performance Prizes and Dynamic Incentives in Best-of-N Contests," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 53(3), pages 563-590, November.
    10. Alex Krumer, 2015. "The Order of Games in a Best-of-Three Contest," Journal of Sports Economics, , vol. 16(2), pages 185-200, February.
    11. Gelder, Alan, 2014. "From Custer to Thermopylae: Last stand behavior in multi-stage contests," Games and Economic Behavior, Elsevier, vol. 87(C), pages 442-466.
    12. Aner Sela & Oz Tsahi, 2020. "On the optimal allocation of prizes in best-of-three all-pay auctions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(2), pages 255-273, August.
    13. Clark, Derek J. & Nilssen, Tore, 2020. "Creating balance in dynamic competitions," International Journal of Industrial Organization, Elsevier, vol. 69(C).
    14. Alex Krumer, 2013. "Best-of-two contests with psychological effects," Theory and Decision, Springer, vol. 75(1), pages 85-100, July.
    15. Peter-J. Jost, 2021. "Competitive Balance and the Away Goals Rule During Extra Time," Journal of Sports Economics, , vol. 22(7), pages 823-863, October.
    16. Sela, Aner & Megidish, Reut, 2014. "Optimal Allocations in Round-Robin Tournaments," CEPR Discussion Papers 9873, C.E.P.R. Discussion Papers.

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    More about this item

    Keywords

    All-pay auctions; Contests;

    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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