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The non-constant-sum Colonel Blotto game

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Listed:
  • Brian Roberson
  • Dmitriy Kvasov
Abstract
The Colonel Blotto game is a two-player constant-sum game in which each player simultaneously distributes his fixed level of resources across a set of contests. In the traditional formulation of the Colonel Blotto game, the players’ resources are “use it or lose it” in the sense that any resources that are not allocated to one of the contests are forfeited. This article examines a non-constant-sum version of the Colonel Blotto game that relaxes this use it or lose it feature. We find that if the level of asymmetry between the players’ budgets is below a threshold, then there exists a one-to-one mapping from the unique set of equilibrium univariate marginal distribution functions in the constant-sum game to those in the non-constant-sum game. Once the asymmetry of the players’ budgets exceeds the threshold, this relationship breaks down and we construct a new equilibrium. Copyright Springer-Verlag 2012

Suggested Citation

  • Brian Roberson & Dmitriy Kvasov, 2012. "The non-constant-sum Colonel Blotto game," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 51(2), pages 397-433, October.
    • Handle: RePEc:spr:joecth:v:51:y:2012:i:2:p:397-433
    DOI: 10.1007/s00199-011-0673-z
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    More about this item

    Keywords

    Colonel Blotto game; All-pay auction; Contests; Mixed strategies; Multi-dimensional contest; C72; D7;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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