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Dynamic contests with resource constraints

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  • Aner Sela
  • Eyal Erez

Abstract

We study a dynamic contest between two players who compete against each other in $$n$$ different stages. The players have winning values for each stage of the contest that may vary across the stages as well as heterogeneous resource budgets that decrease from a given stage to the next proportionally to the resources allocated in that stage. We characterize a subgame perfect equilibrium of this dynamic contest and show that when the winning value is equal between the stages, the players’ resource allocations are weakly decreasing over the stages. We also study the effect of several distributions of winning values on the players’ resource allocations. We show both the distribution of winning values that balances the players’ resource allocations and the distribution of winning values that maximizes the players’ total resource allocations. Copyright Springer-Verlag Berlin Heidelberg 2013

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  • Aner Sela & Eyal Erez, 2013. "Dynamic contests with resource constraints," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(4), pages 863-882, October.
    • Handle: RePEc:spr:sochwe:v:41:y:2013:i:4:p:863-882
    DOI: 10.1007/s00355-012-0711-1
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    Cited by:

    1. Andrea Gallice, 2016. "Optimal stealing time," Theory and Decision, Springer, vol. 80(3), pages 451-462, March.
    2. Nejat Anbarc{i} & Kutay Cingiz & Mehmet S. Ismail, 2020. "Proportional resource allocation in dynamic n-player Blotto games," Papers 2010.05087, arXiv.org, revised Jul 2022.
    3. Klumpp, Tilman & Konrad, Kai A. & Solomon, Adam, 2019. "The dynamics of majoritarian Blotto games," Games and Economic Behavior, Elsevier, vol. 117(C), pages 402-419.
    4. Sela, Aner, 2022. "Effort allocations in elimination tournaments," Economics Letters, Elsevier, vol. 211(C).
    5. Aner Sela, 2017. "Two-stage contests with effort-dependent values of winning," Review of Economic Design, Springer;Society for Economic Design, vol. 21(4), pages 253-272, December.
    6. Anbarci, Nejat & Cingiz, Kutay & Ismail, Mehmet S., 2023. "Proportional resource allocation in dynamic n-player Blotto games," Mathematical Social Sciences, Elsevier, vol. 125(C), pages 94-100.
    7. Malin Arve & Olga Chiappinelli, 2021. "The Role of Budget Constraints in Sequential Elimination Tournaments," Scandinavian Journal of Economics, Wiley Blackwell, vol. 123(4), pages 1059-1087, October.
    8. Aner Sela, 2022. "Ineffective Prizes In Multi-Dimensional Contests," Working Papers 2205, Ben-Gurion University of the Negev, Department of Economics.
    9. Iluz, Asaf & Sela, Aner, 2018. "Sequential contests with first and secondary prizes," Economics Letters, Elsevier, vol. 171(C), pages 6-9.
    10. Jennifer Brown & Dylan B. Minor, 2014. "Selecting the Best? Spillover and Shadows in Elimination Tournaments," Management Science, INFORMS, vol. 60(12), pages 3087-3102, December.
    11. Anbarci, Nejat & Cingiz, Kutay & Ismail, Mehmet, 2018. "Multi-Battle n-Player Dynamic Contests," Research Memorandum 003, Maastricht University, Graduate School of Business and Economics (GSBE).
    12. Dmitry Dagaev & Andrey Zubanov, 2022. "Round-robin tournaments with limited resources," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(3), pages 525-583, October.
    13. 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.
    14. de Roos, Nicolas & Sarafidis, Yianis, 2018. "Momentum in dynamic contests," Economic Modelling, Elsevier, vol. 70(C), pages 401-416.
    15. Masaki Fujimoto, 2023. "A Dynamic Analysis of Equal Revenue Sharing and Endogenous Salary Caps in the N-Team Leagues," Journal of Sports Economics, , vol. 24(5), pages 624-638, June.
    16. Grossmann, Martin & Hottiger, Dieter, 2020. "Liquidity constraints and the formation of unbalanced contests," International Journal of Industrial Organization, Elsevier, vol. 73(C).

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