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The Non-Constant-Sum Colonel Blotto Game

Author

Listed:
  • Brian Roberson
  • Dmitriy Kvasov

Abstract

The Colonel Blotto game is a two-player constant-sum game in which each player simultaneously distributes her 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 which are not allocated to one of the contests are forfeited. This paper examines a non-constant-sum version of the Colonel Blotto game which 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 the unique set of equilibrium univariate marginal distributions of the non-constant-sum game is equivalent up to an affine transformation to the unique set of equilibrium univariate marginal distributions of the constant-sum game. Once the asymmetry of the players’ budgets exceeds the threshold we construct a new equilibrium.

Suggested Citation

  • Brian Roberson & Dmitriy Kvasov, 2008. "The Non-Constant-Sum Colonel Blotto Game," CESifo Working Paper Series 2378, CESifo.
  • Handle: RePEc:ces:ceswps:_2378
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    More about this item

    Keywords

    Colonel Blotto game; all-pay auction; contests;
    All these keywords.

    JEL classification:

    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General

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