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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 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 which are not allocated to one of the contests are forfeited. This article 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 there exists a oneto- 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.

Suggested Citation

  • Brian Roberson & Dmitriy Kvasov, 2010. "The Non-Constant-Sum Colonel Blotto Game," Purdue University Economics Working Papers 1252, Purdue University, Department of Economics.
    • Handle: RePEc:pur:prukra:1252
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    File URL: https://business.purdue.edu/research/Working-papers-series/2010/1252.pdf
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Colonel Blotto Game; All-Pay Auction; Contests; Mixed Strategies;
    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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