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Escape Sensing Games: Detection-vs-Evasion in Security Applications

Niclas Boehmer, Minbiao Han, Haifeng Xu, Milind Tambe

TL;DR

This work introduces Escape Sensing Games (ESGs), a new class of games centered around strategically arranging targets to protect them against a constrained adversary, with motivations from varied domains such as peacekeeping resource transit and cybersecurity.

Abstract

Traditional game-theoretic research for security applications primarily focuses on the allocation of external protection resources to defend targets. This work puts forward the study of a new class of games centered around strategically arranging targets to protect them against a constrained adversary, with motivations from varied domains such as peacekeeping resource transit and cybersecurity. Specifically, we introduce Escape Sensing Games (ESGs). In ESGs, a blue player manages the order in which targets pass through a channel, while her opponent tries to capture the targets using a set of sensors that need some time to recharge after each activation. We present a thorough computational study of ESGs. Among others, we show that it is NP-hard to compute best responses and equilibria. Nevertheless, we propose a variety of effective (heuristic) algorithms whose quality we demonstrate in extensive computational experiments.

Escape Sensing Games: Detection-vs-Evasion in Security Applications

TL;DR

This work introduces Escape Sensing Games (ESGs), a new class of games centered around strategically arranging targets to protect them against a constrained adversary, with motivations from varied domains such as peacekeeping resource transit and cybersecurity.

Abstract

Traditional game-theoretic research for security applications primarily focuses on the allocation of external protection resources to defend targets. This work puts forward the study of a new class of games centered around strategically arranging targets to protect them against a constrained adversary, with motivations from varied domains such as peacekeeping resource transit and cybersecurity. Specifically, we introduce Escape Sensing Games (ESGs). In ESGs, a blue player manages the order in which targets pass through a channel, while her opponent tries to capture the targets using a set of sensors that need some time to recharge after each activation. We present a thorough computational study of ESGs. Among others, we show that it is NP-hard to compute best responses and equilibria. Nevertheless, we propose a variety of effective (heuristic) algorithms whose quality we demonstrate in extensive computational experiments.
Paper Structure (42 sections, 15 theorems, 11 equations, 3 figures, 14 tables, 3 algorithms)

This paper contains 42 sections, 15 theorems, 11 equations, 3 figures, 14 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Our Contribution
  3. Escape Sensing Games (ESGs): The Model
  4. Objectives and equilibrium
  5. A motivating application
  6. Sensor and target types
  7. Related Work
  8. Computational game theory for security
  9. Scheduling
  10. The Algorithmics of Escape Sensing Games
  11. Computing Red's Best Response Strategy
  12. Proof of correctness: forward direction
  13. Proof of correctness: backward direction
  14. Solving for the Stackelberg Equilibrium
  15. Bilevel Optimization
  16. ...and 27 more sections

Key Result

Theorem 1

Best Red Response is NP-complete, even when asked to decide whether Red can sense all targets or not.

Figures (3)

  • Figure 1: A visual representation of an Escape Sensing Game.
  • Figure 2: In this experiment, we focus on the Default setting, but changes the probability of each element $D_{i,j} = 1$. We vary the probability from $0$ to $1$ and observe Blue's utility. We generate 50 random instances with $500$ targets, $10$ sensors, and $\tau=10$ under each setting. Each target's value is drawn within $[0,1]$ uniformly.
  • Figure 3: In this experiment, we generate 50 random instances with $10$ targets, $5$ sensors, and $\tau=2$ under Append game setting. Each target's value is drawn within $[0,1]$ uniformly.

Theorems & Definitions (35)

  • Theorem 1
  • proof
  • Proposition 1
  • proof : Proof Sketch
  • Proposition 2
  • proof
  • Theorem 3
  • Proposition 3
  • Theorem 4
  • proof : Proof Sketch
  • ...and 25 more