### 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.

Original language | English |
---|---|

Pages (from-to) | 397-433 |

Number of pages | 37 |

Journal | Economic Theory |

Volume | 51 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2012 Oct |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Economics and Econometrics

### Cite this

*Economic Theory*,

*51*(2), 397-433. https://doi.org/10.1007/s00199-011-0673-z

**The non-constant-sum Colonel Blotto game.** / Roberson, Brian; Kvasov, Dmitriy.

Research output: Contribution to journal › Article

*Economic Theory*, vol. 51, no. 2, pp. 397-433. https://doi.org/10.1007/s00199-011-0673-z

}

TY - JOUR

T1 - The non-constant-sum Colonel Blotto game

AU - Roberson, Brian

AU - Kvasov, Dmitriy

PY - 2012/10

Y1 - 2012/10

N2 - 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.

AB - 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.

KW - All-pay auction

KW - Colonel Blotto game

KW - Contests

KW - Mixed strategies

KW - Multi-dimensional contest

UR - http://www.scopus.com/inward/record.url?scp=84866751935&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84866751935&partnerID=8YFLogxK

U2 - 10.1007/s00199-011-0673-z

DO - 10.1007/s00199-011-0673-z

M3 - Article

AN - SCOPUS:84866751935

VL - 51

SP - 397

EP - 433

JO - Economic Theory

JF - Economic Theory

SN - 0938-2259

IS - 2

ER -