Can LLMs effectively provide game-theoretic-based scenarios for cybersecurity?

1. Problem Statement

Game theory is a foundational tool in cybersecurity for modeling strategic interactions between attackers and defenders (e.g., intrusion detection, jamming, resource allocation). However, the rapid emergence of Large Language Models (LLMs) as both attackers and defenders introduces a new layer of complexity.

• The Gap: While LLMs are increasingly used to generate scenarios or act as agents in cybersecurity simulations, there is a lack of systematic understanding regarding their actual behavior in game-theoretic settings.
• The Core Question: Do LLM-driven agents behave in alignment with classical game-theoretic predictions (e.g., Nash Equilibria), or do they exhibit unpredictable deviations due to embedded biases, linguistic sensitivities, or personality traits?
• Risk: Indiscriminate use of LLMs in security applications could lead to flawed defense strategies if the models behave differently based on language, geography, or specific model architecture.

2. Methodology

The authors employed a reproducible framework called FAIRGAME to simulate interactions between LLM agents. The study focused on two canonical game types used in cybersecurity:

A. Experimental Setup

• Models Tested: Four state-of-the-art LLMs were evaluated:
  1. GPT-4 (OpenAI, Proprietary)
  2. Gemini Pro 1.5 (Google/DeepMind, Proprietary)
  3. Mistral Large (Mistral AI, Open-source)
  4. Llama 3.1 405B (Meta, Open-source)
• Variables:
  • Languages: English, French, Arabic, Vietnamese, and Mandarin Chinese.
  • Personality Traits: Agents were assigned "Cooperative" or "Selfish" traits.
  • Information State: Agents were tested with knowledge of the total number of rounds (known) vs. unknown.
  • Roles: Agents were kept neutral ("Agent 1", "Agent 2") to avoid role-based bias, though they acted as attackers/defenders implicitly.
• Games Simulated:
  1. One-Shot Zero-Sum Game: Models jamming/eavesdropping or DoS attacks. The goal is to maximize one's own gain while minimizing the opponent's (Payoff sum = 0).
  2. Repeated Prisoner's Dilemma (10 rounds): Models selfishness in multi-hop networks or mutual aid. Agents choose between cooperation and defection over multiple rounds with partial history.

B. Evaluation Metrics

To quantify stability and consistency, the authors defined three metrics:

1. Internal Variability (IV): Variance of outcomes when the same game is played multiple times by the same model (measures internal consistency).
2. Cross-Language Inconsistency (CI): Standard deviation of results when the same game is played in different languages (measures linguistic sensitivity).
3. Variability Over Rounds (VR): Fluctuation in strategy across consecutive rounds in repeated games.

3. Key Results

A. Zero-Sum Game Findings

• Personality Impact: When both agents were "Cooperative," they tended to choose different options, resulting in negative payoffs for the focal agent. This suggests a failure to converge on a mixed strategy or random choice as predicted by game theory.
• Linguistic Sensitivity: Models showed extreme instability when languages changed. For example, GPT-4o behaved as an outlier in English but converged differently in French.
• Stability Ranking: Mistral Large showed the lowest peaks of underperformance and variability. GPT-4o was identified as the least stable model regarding cross-language consistency.

B. Repeated Prisoner's Dilemma Findings

• Convergence to Defection: Generally, LLMs tended to defect (mutual impairment), aligning with the Nash Equilibrium. However, significant deviations occurred based on language and personality.
• Language Bias: Penalties were generally lower (more cooperation) in English and when the number of rounds was unknown. This suggests a bias toward the models' primary training languages.
• Model-Specific Behaviors:
  • Claude 3.5 Sonnet: Showed the highest Cross-Language Inconsistency (CI = 0.79). It converged rapidly to stable values but displayed high sensitivity to language (e.g., cooperating in English but defecting heavily in other languages).
  • GPT-4o & Llama 3: Demonstrated the lowest Cross-Language Inconsistency (CI = 0.37 and 0.42, respectively), indicating more robust behavior across linguistic contexts.
  • Dynamic Evolution: Unlike static predictions, LLMs showed evolving strategies. For instance, GPT-4o started with high cooperation but increased penalties over time, whereas other models showed progressive mutual cooperation.

4. Key Contributions

1. Empirical Validation of LLM Bias: The study provides concrete evidence that LLMs do not strictly adhere to game-theoretic predictions. Their strategies are heavily influenced by language choice and assigned personality traits, which are not factors in traditional mathematical models.
2. Quantitative Benchmarking: The authors introduced and applied specific metrics (IV, CI, VR) to evaluate the reliability of LLMs for security simulations, offering a method to select the most stable models for specific tasks.
3. Framework for Reproducibility: The use and documentation of FAIRGAME provide a standardized, open-source workflow for simulating LLM agents in strategic games, facilitating future research.
4. Warning Against Indiscriminate Deployment: The results highlight that deploying LLMs in cybersecurity without accounting for linguistic and cultural biases could lead to unpredictable defense failures or attacker behaviors.

5. Significance and Implications

• For Cybersecurity Practitioners: The choice of LLM provider and the language of operation are critical security parameters. A model that performs well in English may fail or behave unpredictably in Arabic or Chinese, potentially creating vulnerabilities in global defense systems.
• For AI Safety: The study reveals that "emergent behaviors" in LLMs can be unpredictable. Security strategies based on traditional game theory may be insufficient if the adversary (or defender) is an LLM with non-linear, bias-driven decision-making.
• Future Research Directions: The authors call for:
  • Testing more complex game types (Stackelberg, Markovian, Evolutionary games).
  • Investigating multi-agent networks.
  • Developing "responsible experimentation frameworks" to test LLMs in adversarial settings before deployment.
  • Addressing ethical concerns, such as the potential for LLMs to be used for automated vulnerability discovery or adversarial prompt engineering.

Conclusion: While LLMs offer powerful tools for modeling complex cybersecurity scenarios, they currently lack the stability and predictability required for high-stakes strategic planning. Their behavior is highly sensitive to linguistic and contextual variables, necessitating rigorous, scenario-specific testing before integration into critical security infrastructures.