Feedback Dominance Analysis for Pursuit-Evasion Games on Graphs

2026-10-05

AI Summary

This study addresses the limitations of existing methods for discrete simultaneous-move pursuit-evasion games on graphs, which typically provide only sufficient conditions and rely on open-loop strategies. We propose a novel framework based on set-valued dynamic programming and reachability analysis. By precisely characterizing winning and losing regions, we transform dominating sets into real-time adaptive closed-loop feedback strategies, thereby establishing the first necessary and sufficient conditions for worst-case victory. Furthermore, instantaneous matrix games are introduced to model draw states, enabling the derivation of upper and lower bounds on winning probabilities. Simulations validate the correctness of the characterized dominating regions and the effectiveness of the proposed theoretical bounds, overcoming the inherent bottlenecks of traditional open-loop approaches.

Abstract

This work identifies the dominance regions for discrete, simultaneous-move pursuit-evasion games on graphs. Existing geometric approaches provide efficient characterizations of winning regions, but typically provide only sufficient conditions and rely on open-loop strategies. To address these challenges, we develop a set-based dynamic programming approach to characterize the pursuer's winning and losing regions, providing necessary and sufficient winning conditions under worst-case behavior. The reachability analysis admits a set-chasing interpretation, allowing translation of dominance sets to feedback strategies that adapt to the players'positions in real time. For states where neither player can guarantee victory, we introduce an instantaneous matrix-game formulation and establish upper and lower bounds on the pursuer's winning probability. Simulation results validate the correctness of the dominance-region characterization and the proposed bounds.

Problem

• pursuit-evasion games
• dominance regions
• graphs
• feedback strategies
• winning probability

Innovation

• Pursuit-Evasion Games
• Set-based Dynamic Programming
• Feedback Strategies
• Reachability Analysis
• Matrix Game