The non-constant-sum Colonel Blotto game

Brian Roberson*, Dmitriy Kvasov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

42 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)397-433
Number of pages37
JournalEconomic Theory
Issue number2
Publication statusPublished - 2012 Oct
Externally publishedYes


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

ASJC Scopus subject areas

  • Economics and Econometrics


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