Offline Nash Solvers Meet Online Tree Search in Multi-Agent Games on Graphs

2026-07-09

AI Summary

This work addresses the computational challenge of finding Nash equilibria in multi-agent pursuit-evasion games, where the joint state-action space grows exponentially with the number of agents. To overcome this scalability bottleneck, the authors propose the Primitive-Guided Tree Search (PGTS) framework, which uniquely integrates offline exact subgame Nash equilibrium computation with online Monte Carlo tree search. PGTS decomposes the game into subgames, precomputes optimal policies and value functions offline, and leverages these primitives to guide both tree expansion and leaf evaluation during online search. Evaluated across diverse graph structures—including real-world networks—PGTS significantly outperforms existing learning-based and heuristic approaches, demonstrating superior efficiency, adaptability, and robustness under adversarial perturbations.

Abstract

Computing Nash equilibrium policies in multi-agent Pursuit-Evasion games (PEG) is challenging due to the exponential growth of the joint state and action spaces with the number of agents. Existing approaches either rely on offline equilibrium approximations, which may lack adaptability during execution, or online planning methods, which suffer from large branching factors. In this work, we propose Primitive-Guided Tree Search (PGTS), a hybrid framework that integrates offline exact Nash equilibrium computation with online tree search: PGTS first solves a collection of smaller, tractable sub-games offline; at deployment, PGTS performs online tree search at each time step, using the optimal sub-game policies and value functions to guide tree expansion and estimate leaf-node values. Extensive experiments on varied graph topologies, including real-world networks, demonstrate that PGTS significantly outperforms state-of-the-art learning and heuristic baselines, while maintaining robust performance against adversaries.

Problem

• Nash equilibrium
• multi-agent games
• pursuit-evasion games
• offline solvers
• online tree search

Innovation

• Nash equilibrium
• tree search
• multi-agent games
• offline-online hybrid
• sub-game decomposition