N-Dimensional Blotto Game with Asymmetric Battlefield Values

This paper introduces a new geometric method for constructing equilibrium distributions in the Colonel Blotto game with asymmetric battlefield values, generalizing the construction method of Laslier and Picard (2002). Our method does particularly well in instances of the Colonel Blotto game in which the battlefield values satisfy some clearly defined regularity conditions. The paper establishes the parallel between these conditions and the constrained integer partitioning problem in combinatorial optimisation. We illustrate in the context of the US presidential elections the properties of equilibrium distributions generated by our construction method. In a numerical example, we address the equity of campaign resource allocations.