Approaches to Geo-mathematical Modelling

Chapter 15From Colonel Blotto to Field Marshall Blotto

Peter Baudains, Toby P. Davies, Hannah M. Fry and Alan G. Wilson

15.1 Introduction

Colonel Blotto games (attributed to Borel, 1921; translated in Borel, 1953) consider the strategic allocation of resources under competition with an adversary. They require each player to assign a number of their own resources to a series of different fronts, which represent battlefields over which a conflict takes place. These fronts can be spatial or non-spatial, depending on the application of the model. Each player specifies an allocation of the entirety of their resources across these fronts, and they do so without knowledge of their opponent's allocation. The more resources each player assigns to a particular front, the higher the probability that they will defeat their opponent at that front. In the original application, all that was required for a player to win a particular front was a greater number of their own resources allocated to that front than their opponent. It is then supposed that the player who wins the most battles over the different fronts wins the game overall.

There are a wide range of possible applications of the Colonel Blotto game, but it is often framed as a military problem where the optimal allocation of troops over a series of conflict zones is the objective of a decision maker (the aforenamed Colonel Blotto). In this case, the opponent may represent either a conventional military force or an insurgency. In ...