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Colonel Blotto's Tug of War

Author

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  • Klumpp, Tilman

    (University of Alberta, Department of Economics)

Abstract

We examine Tug of War contests with the Blotto specification. Players have fixed effort budgets and must allocate these budgets to a sequence of battles. The outcome of each battle is a function of the efforts allocated to that battle. The player who first wins L more battles than the opponent wins the contest. We prove the one-step deviation principle for the undiscounted version of this game. We then derive a pure strategy, subgame perfect equilibrium for the case where the contest success function that governs each battle is a generalized Tullock function with exponent 1/2 or less. In the equilibrium, the players invest the same percentage of their remaining resources into each battle. The value of this percentage depends on how close each player is to winning the contest. Escalation of efforts, measured in relation to the players' remaining budgets, occurs when the player with the smaller budget is close to winning. At the same time, the probability that a player wins any individual battle remains constant along the entire equilibrium path.

Suggested Citation

  • Klumpp, Tilman, 2021. "Colonel Blotto's Tug of War," Working Papers 2021-3, University of Alberta, Department of Economics.
    • Handle: RePEc:ris:albaec:2021_003
    as

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    File URL: https://sites.ualberta.ca/~econwps/2021/wp2021-03.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. Baye, Michael R & Kovenock, Dan & de Vries, Casper G, 1994. "The Solution to the Tullock Rent-Seeking Game When R Is Greater Than 2: Mixed-Strategy Equilibria and Mean Dissipation Rates," Public Choice, Springer, vol. 81(3-4), pages 363-380, December.
    3. Konrad, Kai A., 2009. "Strategy and Dynamics in Contests," OUP Catalogue, Oxford University Press, number 9780199549603.
    4. Christopher Budd & Christopher Harris & John Vickers, 1993. "A Model of the Evolution of Duopoly: Does the Asymmetry between Firms Tend to Increase or Decrease?," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 60(3), pages 543-573.
    5. 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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Tug of War games; Colonel Blotto games; sequential contests; multibattle contests;
    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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