The Non-Constant-Sum Colonel Blotto Game

29 Pages Posted: 1 Sep 2008

See all articles by Brian Roberson

Brian Roberson

Purdue University - Department of Economics

Dmitriy Kvasov

Waseda University

Date Written: August 2008

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.

Keywords: Colonel Blotto game, all-pay auction, contests

JEL Classification: C7

Suggested Citation

Roberson, Brian and Kvasov, Dmitriy, The Non-Constant-Sum Colonel Blotto Game (August 2008). CESifo Working Paper Series No. 2378, Available at SSRN: https://ssrn.com/abstract=1261803 or http://dx.doi.org/10.2139/ssrn.1261803

Brian Roberson

Purdue University - Department of Economics ( email )

West Lafayette, IN 47907-1310
United States

Dmitriy Kvasov (Contact Author)

Waseda University ( email )

1-6-1 Nishi-Waseda
Shinjuku-ku, Tokyo 169-8050, Tokyo 169-8050
Japan