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.

翻译：我们运用计算游戏理论来统一基于物理的模型,这些模型在合作和竞争过程中代表一系列代理人的决策。在这里,竞争者试图同时积极影响自己的回报,同时对其竞争者产生消极影响。模拟这些与所谓的博伊德-库拉莫托-兰切斯特(BKL)复杂的动态系统模型的相互作用,可以产生适用于商业、赌博和安全背景的结果。本文研究BKL模型上的一系列决策问题,该模型使用游戏理论方法分析大量的组合、转换动态系统。鉴于其规模,解决这些BKL游戏的计算成本成为解决方案过程中的主导因素。为了解决这个问题,我们引入了新型的Nash Dominant解决器,它既具有数字效率和准确性。这种新的解决方案技术的性能与传统的精确解答器进行了比较,它绕过整个游戏树,并接近了 Myopic 和 Monte Carlo树搜索(MCTS) 等解算器。这些技术被评估,并用于了解非线性动态系统以及战略决策中的非动态环境。