When Lanchester Met Richardson: The Interaction of Warfare with Psychology

Abstract

AbstractSimple dynamical systems, in the spirit of Richardson’s arms race, can be used to investigate the core dynamics of various models of insurgent and multilateral war. This chapter describes two such models. The first combines Richardson’s two-nation arms race with Lanchester’s attrition model and Deitchman’s guerrilla variant of it to create a model in which the typical long-term outcome is neither annihilation nor escalation but rather a stable fixed point, a stalemate. The scaling it implies for the force required to defeat an insurgency matches that which has been observed. The second model is of multilateral attritional war, in the spirit of Richardson’s multinational arms race. We describe the case of three antagonists, whose objective is to win but, if they cannot win, to minimize their remaining opponents. In contrast to truels and triads in which the objective is survival, and the weakest actor often emerges in a position of surprising strength, here the outcome is mutual annihilation, unless one side can beat the others put together.