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Sequential Majoritarian Blotto Games

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  • Tilman Klumpp
  • Kai A. Konrad

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 battleï¬ eld and of the number of victories and losses the player accumulated in prior battles. This result is in stark contrast to equilibrium behavior in sequential contests that do not involve either ï¬ xed 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 games resembles an all-pay auction without noise.

Suggested Citation

  • Tilman Klumpp & Kai A. Konrad, 2018. "Sequential Majoritarian Blotto Games," Working Papers tax-mpg-rps-2018-05, Max Planck Institute for Tax Law and Public Finance.
    • Handle: RePEc:mpi:wpaper:tax-mpg-rps-2018-05
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    References listed on IDEAS

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    1. Konrad, Kai A., 2009. "Strategy and Dynamics in Contests," OUP Catalogue, Oxford University Press, number 9780199549603.
    2. Tilman Klumpp & Hugo M. Mialon & Michael A. Williams, 2015. "Leveling the Playing Field? The Role of Public Campaign Funding in Elections," American Law and Economics Review, American Law and Economics Association, vol. 17(2), pages 361-408.
    3. Deck, Cary & Sheremeta, Roman, 2012. "Fight or Flight?," MPRA Paper 52130, University Library of Munich, Germany.
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    5. 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.
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    9. David A. Malueg & Andrew J. Yates, 2010. "Testing Contest Theory: Evidence from Best-of-Three Tennis Matches," The Review of Economics and Statistics, MIT Press, vol. 92(3), pages 689-692, August.
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    Cited by:

    1. Qianqian Kong & Hans Peters, 2023. "Sequential claim games," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 45(3), pages 955-975, September.
    2. 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.

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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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