A Mean-Field Game model for large-scale attrition in attacker–defender systems

In this talk I present a novel Mean-Field Game (MFG) framework for large-scale attacker–defender systems aimed at protecting one or multiple High-Value Units (HVUs). Motivated by classical agent-wise attrition models, we introduce a population-wise attrition mechanism formulated by statistical distance between populations, enabling a macroscopic description of weapon-based interactions between large populations. Leveraging this and Lions derivative on the space of probability measures, we derive the associated MFG system, which characterizes optimal strategies and the evolution of population distributions in attacker–defender interactions. For numerical investigation, we develop a numerical scheme combining physics-informed neural networks with the Sinkhorn algorithm to solve our attacker–defender MFG system.