A Mean-Field Game Model For Large-Scale Attrition in Attacker-Defender Systems

TL;DR

This paper introduces a novel mean-field game framework for modeling large-scale attacker-defender interactions, using population-wise attrition mechanisms and advanced numerical methods to analyze strategic behaviors.

Contribution

The paper develops a new MFG model incorporating population-wise attrition and statistical distances, with a combined neural network and Sinkhorn numerical scheme for analysis.

Findings

The model provides bounds on defender density ensuring physical realism.

Simulations show sensitivity of outcomes to weapon strength and population dispersion.

The framework effectively captures strategic dynamics in large-scale attacker-defender systems.

Abstract

This paper proposes 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. We analyze the model by establishing upper and lower bounds on the defender density, ensuring physical consistency by preventing concentration and depletion. For numerical investigation, we develop a numerical scheme combining physics-informed neural networks with Sinkhorn method to solve attacker-defender MFG system. Simulations confirm the effectiveness of the framework and reveal key insights, including sensitivity to weapon strengths and population dispersion.