Lanchester Law Model with Fractional Distribution of Fire and Variable Performance Against Multiple Opponents

Lanchester’s law serves as a deterministic mathematical model of a battle between two or more opponents. We build a new model that incorporates both variable offense and variable defense, as well as the commander’s ability to focus fire on a selected enemy. We show that in a situation where an army fights two allies, the correct strategy of focusing on the weaker enemy leads to an eventual win, whereas the incorrect decision to split the fire equally leads to the army’s annihilation.