Unifying warfighting functions in mathematical modelling: combat, manoeuvre, and C2

Adversarial Decisions on Complex Dynamical Systems using Game Theory

“…Instead the numerically superior Blue player exhibits a 'sweet spot' at ζ B ≈ 0.7, with further increases to ζ B producing diminishing results across all choices of ζ R . This is consistent with previous work [21], as excessive internal coupling in relation to the internal structure and other variables leads to a 'rigidity' in the system. A similar point of diminished returns exists also for Red beyond the range of ζ R considered here, where the broader range is a consequence of the higher connectivity of Red compared to the hierarchical structure of Blue.…”

“…Next, we incorporate into this the well-known Lanchester model to provide the combined BKL Model. This summarises the original proposal in [21].…”

“…Note that this model may be called a global model, where the resources of the two sides are homogeneous. In [21] a heterogeneous form of the model is also given, where the resources may also be structured through network parameters using the generalisation of the Lanchester model in [26]. We do not treat this model here in this first application of computational game Theory to such a system.…”

“…As a representation of growth and decay of entities, these models describe physical processes often obeying conservation laws, with wide application in ecology [20]. The unification of these models, Kuramoto and Lanchester, was first proposed in [21], and in this context is called the Boyd-Kuramoto-Lanchester (BKL) dynamical system. In essence, because both models admit treatment in continuous-time differential equations their unification is entirely natural.…”

“…This model of two players engaged in adversarial decision making under constrained resources rewards internal synchronisation, but also incorporates the potential for adversary driven outcomes that undermine the capacity for coupling. The competitive nature of these components creates a process that is inherently Game-Theoretic in nature [21], and exists alongside other recent works tying dynamical systems to Game-Theory [22]. Due to their successful application to multiple adversarial environments, the mathematical and conceptual framework of Security Games [23] is applied to two-player adversarial BKL games.…”