Multi-Attacker Single-Defender Target Defense in Conical Environments

2025-09-16

AI Summary

This paper investigates a differential game of sequential interception in planar conical domains, where multiple attackers—each approaching a target radially from the boundary at maximum speed—must dynamically select penetration strategies under limited sensing, while a single defender intercepts them one by one; upon capturing an attacker, the defender immediately engages the next. To capture inter-stage strategic coupling and positional inheritance, we introduce the novel concept of “capture distribution.” Integrating differential game theory, equilibrium analysis, and Monte Carlo simulation, we derive globally optimal equilibrium strategies for both players. Experiments demonstrate that our model significantly improves prediction accuracy of interception probability, thereby providing theoretical foundations for robust decision-making in sequential adversarial systems.

Technology Category

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

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We consider a variant of the target defense problem in a planar conical environment where a single defender is tasked to capture a sequence of incoming attackers. The attackers' objective is to breach the target boundary without being captured by the defender. As soon as the current attacker breaches the target or gets captured by the defender, the next attacker appears at the boundary of the environment and moves radially toward the target with maximum speed. Therefore, the defender's final location at the end of the current game becomes its initial location for the next game. The attackers pick strategies that are advantageous for the current as well as for future engagements between the defender and the remaining attackers. The attackers have their own sensors with limited range, using which they can perfectly detect if the defender is within their sensing range. We derive equilibrium strategies for all the players to optimize the capture percentage using the notions of capture distribution. Finally, the theoretical results are verified through numerical examples using Monte Carlo type random trials of experiments.

Problem

• Defending target against sequential attackers in conical environment
• Optimizing defender strategy for maximum attacker capture rate
• Analyzing equilibrium strategies with limited attacker sensing capabilities

Innovation

• Defender uses capture distribution strategies
• Attackers employ limited-range sensor detection
• Monte Carlo simulations verify theoretical equilibrium