Dominance Regions of Pursuit-evasion Games in Non-anticipative Information Patterns

2025-02-05

AI Summary

This paper addresses the characterization and control of the evader’s initial advantage region in pursuit-evasion games under non-anticipative information patterns. Specifically, it tackles the fundamental question of whether the evader can exit its initial dominance region before capture. The work establishes, for the first time, that this region coincides precisely with the evader’s open-loop reachable set. For obstacle-free environments, it proves the existence of non-anticipative capture strategies; for environments with obstacles, it derives necessary conditions for strategy existence and provides sufficient conditions for single-corner obstacles. Methodologically, the approach integrates geometric analysis, optimal path theory, differential game theory, and reachable set modeling. The results lay a theoretical foundation for non-anticipative pursuit-evasion games and provide verifiable existence criteria and a systematic design framework for obstacle-constrained pursuit-evasion and target-defense games.

Technology Category

• Search and Optimization: Adversarial Search
• Game Theory and Economic Paradigms: Adversarial Learning
• Multiagent Systems: Adversarial Agents

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Tracking, profiling, and countermeasures against them
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

The evader's dominance region is an important concept and the foundation of geometric methods for pursuit-evasion games. This article mainly reveals the relevant properties of the evader's dominance region, especially in non-anticipative information patterns. We can use these properties to research pursuit-evasion games in non-anticipative information patterns. The core problem is under what condition the pursuer has a non-anticipative strategy to prevent the evader leaving its initial dominance region before being captured regardless of the evader's strategy. We first define the evader's dominance region by the shortest path distance, and we rigorously prove for the first time that the initial dominance region of the evader is the reachable region of the evader in the open-loop sense. Subsequently, we prove that there exists a non-anticipative strategy by which the pursuer can capture the evader before the evader leaves its initial dominance region's closure in the absence of obstacles. For cases with obstacles, we provide a counter example to illustrate that such a non-anticipative strategy does not always exist, and provide a necessary condition for the existence of such strategy. Finally, we consider a scenario with a single corner obstacle and provide a sufficient condition for the existence of such a non-anticipative strategy. At the end of this article, we discuss the application of the evader's dominance region in target defense games. This article has important reference significance for the design of non-anticipative strategies in pursuit-evasion games with obstacles.

Problem

• Defines evader's dominance region using shortest path distance.
• Proves pursuer's non-anticipative strategy existence without obstacles.
• Provides conditions for strategy existence with obstacles.

Innovation

• Defines evader's dominance region
• Proves non-anticipative strategy existence
• Analyzes obstacle impact strategy