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On the optimal allocation of prizes in best-of-three all-pay auctions

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  • Aner Sela

    (Ben-Gurion University of the Negev)

  • Oz Tsahi

    (Ben-Gurion University of the Negev)

Abstract

We study best-of-three all-pay auctions with two players who compete in three stages with a single match per stage. The first player to win two matches wins the contest. We assume that a prize sum is given, and show that if players are symmetric, the allocation of prizes does not have any effect on the players’ expected total effort. On the other hand, if players are asymmetric, in order to maximize the players’ expected total effort, independent of the players’ types, it is not optimal to allocate a single final prize to the winner. Instead, it is optimal to allocate intermediate prizes in the first stage or/and in the second stage in addition to the final prize. When the asymmetry of the players’ types is sufficiently high, it is optimal to allocate intermediate prizes in both two first stages and a final prize to the winner.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sochwe:v:55:y:2020:i:2:d:10.1007_s00355-020-01239-1
    DOI: 10.1007/s00355-020-01239-1
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    Cited by:

    1. Aner Sela, 2021. "Resource Allocations In Multi-Stage Contests," Working Papers 2105, Ben-Gurion University of the Negev, Department of Economics.
    2. 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.
    3. Juan Beccuti & Marc M ller, 2020. "Fighting for Lemons: The Encouragement Effect in Dynamic Contests with Private Information," Diskussionsschriften dp2017, Universitaet Bern, Departement Volkswirtschaft.
    4. Aner Sela, 2022. "Ineffective Prizes In Multi-Dimensional Contests," Working Papers 2205, Ben-Gurion University of the Negev, Department of Economics.
    5. 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.
    6. Feng, Xin & Jiao, Qian & Kuang, Zhonghong & Lu, Jingfeng, 2024. "Optimal prize design in team contests with pairwise battles," Journal of Economic Theory, Elsevier, vol. 215(C).
    7. 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.

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