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The dynamics of majoritarian Blotto games

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  • Klumpp, Tilman
  • Konrad, Kai A.
  • Solomon, Adam

Abstract

We study Colonel Blotto games with sequential battles and a majoritarian objective. For a large class of contest success functions, the equilibrium is unique and characterized by an even split: Each battle that is reached before one of the players wins a majority of battles is allocated the same amount of resources from the player's overall budget. As a consequence, a player's chance of winning any particular battle is independent of the battlefield and of the number of victories and losses the player has accumulated in prior battles. This result is in stark contrast to equilibrium behavior in sequential contests that do not involve either fixed budgets or a majoritarian objective. We also consider the equilibrium choice of an overall budget. For many contest success functions, if the sequence of battles is long enough the payoff structure in this extended game resembles an all-pay auction without noise.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:gamebe:v:117:y:2019:i:c:p:402-419
    DOI: 10.1016/j.geb.2019.07.004
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    Cited by:

    1. Li, Xinmi & Zheng, Jie, 2022. "Pure strategy Nash Equilibrium in 2-contestant generalized lottery Colonel Blotto games," Journal of Mathematical Economics, Elsevier, vol. 103(C).
    2. Daniel Graydon Stephenson, 2023. "Multi-battle contests over complementary battlefields," Working Papers 2303, VCU School of Business, Department of Economics.
    3. Giuseppe Di Liddo & Annalisa Vinella, 2022. "Asymmetric yardstick competition: traditional procurement versus public-private partnerships," Italian Economic Journal: A Continuation of Rivista Italiana degli Economisti and Giornale degli Economisti, Springer;Società Italiana degli Economisti (Italian Economic Association), vol. 8(3), pages 669-695, November.
    4. Konishi, Hideo & Pan, Chen-Yu & Simeonov, Dimitar, 2022. "Equilibrium player choices in team contests with multiple pairwise battles," Games and Economic Behavior, Elsevier, vol. 132(C), pages 274-287.
    5. Nicolas Houy & Jean-Philippe Nicolaï & Marie Claire Villeval, 2020. "Always doing your best? Effort and performance in dynamic settings," Theory and Decision, Springer, vol. 89(3), pages 249-286, October.
    6. 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.
    7. Brian Roberson & Oz Shy, 2021. "Costly force relocation in the Colonel Blotto game," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(1), pages 39-52, April.
    8. Shy, Oz, 2021. "Multimarket lobbying with reserves," Mathematical Social Sciences, Elsevier, vol. 109(C), pages 106-112.
    9. 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.
    10. Aner Sela, 2022. "Ineffective Prizes In Multi-Dimensional Contests," Working Papers 2205, Ben-Gurion University of the Negev, Department of Economics.
    11. Di Liddo, Giuseppe & Vinella, Annalisa, 2024. "Global public good provision in emergency states: A model of (asymmetric) yardstick competition between rent-seeking governments," Socio-Economic Planning Sciences, Elsevier, vol. 93(C).
    12. 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.
    13. Lu, Jingfeng & Lu, David, 2020. "Task arrangement in team competitions," Economics Letters, Elsevier, vol. 193(C).
    14. 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.
    15. Maria Arbatskaya & Hideo Konishi, 2021. "Dynamic Team Contests with Complementary Efforts," Boston College Working Papers in Economics 1033, Boston College Department of Economics.
    16. 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).
    17. Aner Sela, 2024. "Intermediate prizes in multi-dimensional contests," Theory and Decision, Springer, vol. 97(4), pages 721-743, December.
    18. Louis-Sidois, Charles, 2024. "Buying winners," Games and Economic Behavior, Elsevier, vol. 143(C), pages 1-11.

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    More about this item

    Keywords

    Blotto games; Dynamic battles; Multi-battle contest; All-pay auctions; Sequential elections;
    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

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