Game theory deals with the mathematical modelling of conflict and cooperation. Formal mathematical analysis of conflict emerged from World War I in the writings of Frederick Lanchester (1868-1946) and Lewis Richardson (1881-1953). Their concerns were sharply distinct—those of war and of peace. Lanchester’s Aircraft in Warfare (1916) examined how to win battles by choice of appropriate strategy such as concentration of forces. Richardson was a pacifist Quaker who, from his Mathematical Psychology of War (1919) onward, attempted to understand the dynamics of arms races and the statistics of outbreaks of war as aids to preventing war.
Lanchesters and Richardson’s work is of particular interest. While strategic and tactical manuals for military commanders have been plentiful from a very early period, formal models in this area are lacking. Such manuals typically focus on peace if it is a peace that comes with victory, but not the prevention of conflict per se. Even chess, a ‘war game’ sometimes said to have been invented to produce peace, accomplishes this only when a leader playing with a potential opponent exhibits overwhelmingly superior strategic ability.
This makes Richardson’s work especially surprising. Not only did he analyse conflict in order to produce peace, but his proposed methods of propagating peace included education in general and wider education in foreign languages. He constructed mathematical models aimed to persuade readers of factors which favour relatively prompt conflict and of the disastrous consequences of conflict.
The second feature of particular interest in the work of Lanchester and Richardson is their common modelling method: one in which they constructed what might now be called differential games. 2 While chess and most other war games are games of attrition, no previous analysis of strategic interdependence had focused on factor flows as decision variables or determinants of ‘success’. Lanchester and Richardson innovated this new approach.
In the first section, we discuss the early and celebrated war manual of Sun Tzu, The Art of War. The second addresses Lanchester’s models and the third, Richardson’s.