N-dimensional Colonel Blotto Game with Asymmetric Battlefield Values

Abstract

This paper describes a geometrical method for constructing equilibrium distribution in the Colonel Blotto game with asymmetric battlefield values. It generalises to the n-dimensional case a construction method first described by Gross and Wagner. The proposed method does particularly well in instances of the Colonel Blotto game in which the battlefield weights satisfy some clearly defined regularity conditions. Though these conditions constrain the set of games in which this method reliably generates equilibrium strategies, they are less restrictive than the condition of symmetry across all battlefields, hitherto common in the literature. The paper also explores the parallel between these conditions and the integer partitioning problem in combinatorial optimisation.