Adversarial Decisions on Complex Dynamical Systems using Game Theory

TL;DR

This paper introduces a novel Nash Dominant solver for complex adversarial decision-making in large-scale dynamical systems modeled by the BKL framework, improving computational efficiency and accuracy over traditional methods.

Contribution

The paper presents a new Nash Dominant solver that efficiently and exactly solves large BKL game models, outperforming existing exact and approximate solvers.

Findings

The Nash Dominant solver is more computationally efficient than traditional methods.

The solver provides exact solutions for large-scale BKL games.

Insights into strategic decision making in complex dynamical systems are gained.

Abstract

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.