Economic Theory

, Volume 51, Issue 2, pp 397–433 | Cite as

The non-constant-sum Colonel Blotto game

  • Brian RobersonEmail author
  • Dmitriy Kvasov


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.


Colonel Blotto game All-pay auction Contests Mixed strategies Multi-dimensional contest 

JEL Classification

C72 D7 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of Economics, Krannert School of ManagementPurdue UniversityWest LafayetteUSA
  2. 2.School of EconomicsUniversity of AdelaideAdelaideAustralia

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