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Gamu Blue: A Practical Tool for Game Theory Security Equilibria

Ameer Taweel, Burcu Yıldız, Alptekin Küpçü

TL;DR

The paper presents Gamu Blue, a practical Python-based tool built on Gambit to compute multiple multi-party security equilibria definitions in cybersecurity games, including $k$-resiliency, $l$-repellence, $t$-immunity, $(l,t)$-resistance, and $m$-stability. It formalizes the underlying $n$-player normal-form framework, contrasts old and new definitions, and provides concrete algorithms with worst-case time bounds, highlighting PPAD-hardness where relevant. Through experiments on IOC and FD games, it demonstrates how the tool exposes the security properties of different mechanisms and characterizes their computational scalability, offering open-source code as a baseline for future work. Overall, Gamu Blue enables researchers to analyze and compare security equilibria in a consistent, reproducible manner, accelerating practical assessments and algorithmic improvements in game-theoretic cybersecurity.

Abstract

The application of game theory in cybersecurity enables strategic analysis, adversarial modeling, and optimal decision-making to address security threats' complex and dynamic nature. Previous studies by Abraham et al. and Biçer et al. presented various definitions of equilibria to examine the security aspects of games involving multiple parties. Nonetheless, these definitions lack practical and easy-to-use implementations. Our primary contribution is addressing this gap by developing Gamu Blue, an easy-to-use tool with implementations for computing the equilibria definitions including k-resiliency, l-repellence, t-immunity, (l, t)-resistance, and m-stability.

Gamu Blue: A Practical Tool for Game Theory Security Equilibria

TL;DR

The paper presents Gamu Blue, a practical Python-based tool built on Gambit to compute multiple multi-party security equilibria definitions in cybersecurity games, including -resiliency, -repellence, -immunity, -resistance, and -stability. It formalizes the underlying -player normal-form framework, contrasts old and new definitions, and provides concrete algorithms with worst-case time bounds, highlighting PPAD-hardness where relevant. Through experiments on IOC and FD games, it demonstrates how the tool exposes the security properties of different mechanisms and characterizes their computational scalability, offering open-source code as a baseline for future work. Overall, Gamu Blue enables researchers to analyze and compare security equilibria in a consistent, reproducible manner, accelerating practical assessments and algorithmic improvements in game-theoretic cybersecurity.

Abstract

The application of game theory in cybersecurity enables strategic analysis, adversarial modeling, and optimal decision-making to address security threats' complex and dynamic nature. Previous studies by Abraham et al. and Biçer et al. presented various definitions of equilibria to examine the security aspects of games involving multiple parties. Nonetheless, these definitions lack practical and easy-to-use implementations. Our primary contribution is addressing this gap by developing Gamu Blue, an easy-to-use tool with implementations for computing the equilibria definitions including k-resiliency, l-repellence, t-immunity, (l, t)-resistance, and m-stability.
Paper Structure (11 sections, 10 figures, 2 tables, 4 algorithms)

This paper contains 11 sections, 10 figures, 2 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Basics
  4. Multi-Party Secure Equilibria Definitions Introduced In old-definitions
  5. Improved Multi-Party Secure Equilibria Definitions Introduced In new-definitions
  6. Algorithms
  7. Experimental Results
  8. Multi-Party Games
  9. Input Format
  10. Timing Benchmarks
  11. Conclusion

Figures (10)

  • Figure 1: IOC Represented in NFG Format For 3 Players
  • Figure 2: IOC Represented in AGG Format For 3 Players
  • Figure 3: FD Represented in NFG Format For 3 Players
  • Figure 4: FD Represented in AGG Format For 3 Players
  • Figure 5: Experimental Performance of $k$-resiliency
  • ...and 5 more figures

Theorems & Definitions (11)

  • Definition 1: $n$-Player Normal-Form Game
  • Definition 2: Nash Equilibrium
  • Definition 3: Weakly Dominant Strategy of a Player
  • Definition 4: Coalition Utility
  • Definition 5: Weakly Dominant Strategy of a Coalition
  • Definition 6: $k$-resiliency
  • Definition 7: $t$-immunity
  • Definition 8: $(k, t)$-robustness
  • Definition 9: $\ell$-repellence
  • Definition 10: $(\ell, t)$-resistance
  • ...and 1 more