Non-Monotonicity, Chaos and Combat Models

While few combat modelers claim absolution predictivity for their models, many suggest that their models are good at relative prediction – indicating when one system or configuration is better than another. Relative predictivity requires a model to be monotonic in its outcomes – each additional increment of combat power for one combatant must lead to at least as good an outcome. This report shows that nonlinearities in very simple deterministic combat models can produce non-monotonic results, where an additional increment of combat power leads to worse results. It further relates these non-monotonicities to the chaos that can bedevil nonlinear systems.