  We apply computational Game Theory to a unification of physics-based models
that represent decision-making across a number of agents within both
cooperative and competitive processes. Here the competitors try to both
positively influence their own returns, while negatively affecting those of
their competitors. Modelling these interactions with the so-called
Boyd-Kuramoto-Lanchester (BKL) complex dynamical system model yields results
that can be applied to business, gaming and security contexts. This paper
studies a class of decision problems on the BKL model, where a large set of
coupled, switching dynamical systems are analysed using game-theoretic methods.
  Due to their size, the computational cost of solving these BKL games becomes
the dominant factor in the solution process. To resolve this, we introduce a
novel Nash Dominant solver, which is both numerically efficient and exact. The
performance of this new solution technique is compared to traditional exact
solvers, which traverse the entire game tree, as well as to approximate solvers
such as Myopic and Monte Carlo Tree Search (MCTS). These techniques are
assessed, and used to gain insights into both nonlinear dynamical systems and
strategic decision making in adversarial environments.
