Multi-Defender Single-Attacker Perimeter Defense Game on a Cylinder: Special Case in which the Attacker Starts at the Boundary

2026-02-13 · Source: cs.MA updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Robotics & Autonomous Systems · Depth: Advanced, extended

Summary

Michael Otte and Roderich Groß present a multi-agent perimeter defense game on a cylinder, focusing on a special case where a single fast-moving attacker starts infinitesimally close to a defended boundary segment. A team of 'n' slow-moving, homogeneous defenders, each with an identically sized defensive region and constant velocity, must prevent the attacker from crossing the perimeter. The authors derive closed-form expressions to determine the conditions under which the attacker will win, even when defenders are optimally positioned and coordinated. These expressions quantify the trade-offs between the number of defenders, their velocities, and their defensive range, considering the perimeter length and attacker's velocity. The cylindrical model serves as a limiting case for other 1-D perimeter defense scenarios, such as circular boundaries.

Key takeaway

For AI Scientists designing multi-agent security systems, understanding the derived closed-form expressions is crucial for predicting system vulnerabilities. You should use these formulas to quantify the maximum defendable perimeter length based on defender count, speed, and defensive range, especially when an attacker starts at a guarded boundary segment. This allows for informed decisions on resource allocation and strategic positioning to prevent infiltration.

Key insights

Closed-form expressions determine attacker win conditions in a multi-defender perimeter defense game on a cylinder.

Principles

• Optimal defense requires coordinated defender movement.
• Cylindrical perimeters approximate other 1-D boundaries.
• Attacker wins if perimeter length exceeds maximum defendable length.

Method

The method involves deriving closed-form expressions for attacker win conditions by analyzing two symmetric starting configurations for homogeneous defenders, assuming optimal positioning and coordination.

In practice

• Quantify defender count vs. speed trade-offs.
• Evaluate perimeter security based on agent parameters.
• Apply formulas to 1-D boundary defense scenarios.

Topics

• Multi-Agent Systems
• Perimeter Defense Games
• Game Theory
• Optimal Strategies
• Differential Games

Best for: AI Scientist, AI Researcher, Robotics Engineer, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.MA updates on arXiv.org.