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How to split the pie: Optimal rewards in dynamic multi-battle competitions

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  • Feng, Xin
  • Lu, Jingfeng

Abstract

Multi-battle competitions are ubiquitous in real life. In this paper, we examine the effort-maximizing reward design in sequentially played multi-battle competitions between two players. The organizer has a fixed prize budget, and rewards players contingent on the number of battles they win in a three-battle contest. A full spectrum of contest technologies in the Tullock family is accommodated. We find that the optimal design varies with the discriminatory power of the contest technology. In particular, when it is in the low range, winner-take-all is optimal. For the intermediate range, as discriminatory power increases, the optimal prize structure evolves continuously from winner-take-all to the proportional-division rule due to the need to mitigate the growing momentum/discouragement effect. For the high range, a wide span of prize structures extracts full surplus and is thus optimal. Several robustness checks confirm that mitigating the momentum/discouragement effect is essential for effort-maximizing prize design in dynamic multi-battle contests.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:pubeco:v:160:y:2018:i:c:p:82-95
    DOI: 10.1016/j.jpubeco.2018.03.003
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    1. Letina, Igor & Liu, Shuo & Netzer, Nick, 2023. "Optimal contest design: Tuning the heat," Journal of Economic Theory, Elsevier, vol. 213(C).
    2. Barbieri, Stefano & Serena, Marco, 2024. "Winner's effort in multi-battle team contests," Games and Economic Behavior, Elsevier, vol. 145(C), pages 526-556.
    3. 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.
    4. Aner Sela, 2022. "Ineffective Prizes In Multi-Dimensional Contests," Working Papers 2205, Ben-Gurion University of the Negev, Department of Economics.
    5. Derek J. Clark & Tore Nilssen & Jan Yngve Sand, 2020. "Gaining advantage by winning contests," Review of Economic Design, Springer;Society for Economic Design, vol. 24(1), pages 23-38, June.
    6. Huang, Lingbo & Murad, Zahra, 2021. "Fighting alone versus fighting for a team: An experiment on multiple pairwise contests," Journal of Economic Behavior & Organization, Elsevier, vol. 183(C), pages 616-631.
    7. Haoming Liu & Jingfeng Lu & Alberto Salvo, 2023. "Willingness to fight on: Environmental quality in dynamic contests," RAND Journal of Economics, RAND Corporation, vol. 54(2), pages 189-239, June.
    8. 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).
    9. 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.
    10. 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.
    11. Clark, Derek J. & Nilssen, Tore, 2020. "Creating balance in dynamic competitions," International Journal of Industrial Organization, Elsevier, vol. 69(C).
    12. Huang, Ying & Jiao, Qian & Shen, Bo & Sun, Xiang, 2023. "Conflicts in regular networks," Journal of Mathematical Economics, Elsevier, vol. 106(C).
    13. Alshech, Shahar & Sela, Aner, 2021. "The optimal allocation of prizes in two-stage contests," Economics Letters, Elsevier, vol. 203(C).
    14. Barbieri, Stefano & Serena, Marco, 2022. "Biasing dynamic contests between ex-ante symmetric players," Games and Economic Behavior, Elsevier, vol. 136(C), pages 1-30.

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    More about this item

    Keywords

    Effort maximization; Multi-battle contest; Proportional-division rule; Split-award; Winner-take-all;
    All these keywords.

    JEL classification:

    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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