Multi-Player Pursuit-Evasion Game With Interaction Constraints: A Cooperative Game Theoretic Approach Based on Coalition Structure

This paper presents a comprehensive mathematical approach to address the multi-player and multi-objective pursuit-evasion games problem, incorporating coalition structure constraints from a cooperation-competition perspective. Social interaction networks are developed to approximate priority communication alliances based on individual pReferences, establishing a multi-connected topology and decision space for the games. An N-player variable-sum differential game model, featuring autonomous obstacle avoidance, is formulated by integrating kinematic constraints and the social forces method. Rigorous proofs are provided for the uniqueness of payoff distribution, the stability of alliance structures, and the convergence of many-to-many differential games to Nash Equilibrium. Simulation and experimental results are presented to validate the effectiveness and performance of the proposed method. Note to Practitioners-A structured stable alliance is essential for fostering collective intelligence, especially in scenarios marked by intense conflict and the necessity for cooperation. While traditional methods (e.g., optimal control, differential games) are widely studied, many rely on rigid, random, or preassigned large-scale alliances that miss dynamic group interactions and cooperative alliance dynamics, leading to inefficient resource allocation. Drawing inspiration from social force models, we propose a novel coalition-structure-based cooperative game theory framework. By integrating multi-agent interactions via a coupled differential game on interconnected topologies, it offers new perspectives for multi-agent pursuit-evasion with obstacles and coalition constraints, advancing collective intelligence research in military defense, law enforcement, and maritime surveillance-domains where group dynamics are critical.