THE LANCHESTER SQUARE-LAW MODEL EXTENDED TO A (2,2) CONFLICT

A natural extension of the Lanchester (1, 1) square-law model is the (M, N) linear model in which M forces oppose N forces with constant attrition rates. The (2, 2) model is treated from both direct and inverse viewpoints. The inverse problem means that the model is to be fitted to a minimum number of observed force levels, i.e. the attrition rates are to be found from the initial force levels together with the levels observed at two subsequent times. An approach based on Hamiltonian dynamics has enabled the authors to derive a procedure for solving the inverse problem, which is readily computerized. Conflicts in which participants unexpectedly rally or weaken must be excluded.