A Game-Theoretic Utility Network for Cooperative Multi-Agent Decisions in Adversarial Environments

Many underlying relationships among multi-agent systems (MAS) in various scenarios, especially agents working on dangerous, hazardous, and risky situations, can be represented in terms of game theory. In adversarial environments, the adversaries can be intentional or unintentional based on their needs and motivations. Agents will adopt suitable decision-making strategies to maximize their current needs and minimize their expected costs. In this paper, we propose a new network model called Game-Theoretic Utility Tree (GUT) to achieve cooperative decision-making for MAS in adversarial environments combining the core principles of game theory, utility theory, and probabilistic graphical models. Through calculating multi-level Game-Theoretic computation units, GUT can decompose high-level strategies into executable lower levels. Then, we design Explorers and Monsters Game to validate our model against a cooperative decision-making algorithm based on the state-of-the-art QMIX approach. Also, we implement different predictive models for MAS working with incomplete information to estimate adversaries' state. Our experimental results demonstrate that the GUT significantly enhances cooperation among MAS to successfully complete the assigned tasks with lower costs and higher winning probabilities against adversaries