External Attention Bridge (EAB) Framework

• The paper introduces a novel methodology that bridges external signals with internal LLM dynamics, enhancing interpretability and strategic agent behavior.
• It employs a modular simulation engine using declarative JSON configurations and language-adapted prompts to orchestrate multi-agent interactions and record detailed behavioral logs.
• Through rigorous statistical analysis and supervised strategy recognition, the framework enables real-time auditing, benchmarking, and bias detection in AI systems.

The FAIRGAME framework comprises a family of methodologies and software systems for the game-theoretic auditing, analysis, and governance of AI agents, particularly LLMs, in multi-agent strategic and social environments. Originating as the "Framework for AI Agents’ Bias Recognition using Game Theory," FAIRGAME treats LLMs as fully fledged strategic agents, orchestrates repeated interactions in formal normal-form games, records complete behavioral histories, and analyzes emergent biases, strategic intentions, and equilibrium behaviors with rigorous statistical and game-theoretic tools. Extensions of FAIRGAME incorporate payoff-scaled social dilemmas, multi-agent generalizations, and supervised strategy recognition, providing a unified pipeline for systematic and reproducible agent auditing, benchmarking, and intervention in socio-technical systems (Huynh et al., 8 Dec 2025, Buscemi et al., 19 Apr 2025, Buscemi et al., 30 Jul 2025).

1. Architecture and Core Methodology

FAIRGAME splits game simulation into two independent axes: (i) a declarative JSON-based configuration specifying game structure (payoff matrices, horizon $T$, language, personalities, model backends) and (ii) parameterized, language-adapted prompt templates injected with current state and history at each step. The runtime instantiates LLM agents with specified “personalities” and allocates them to roles. Each agent receives prompts filled with the current payoff table, full joint history, and any relevant meta-information (e.g., other agents’ known traits). On receiving textual output, FAIRGAME parses these into discrete actions, computes payoffs, updates the log, and proceeds to the next period.

The simulation engine supports both two-agent (canonical) matrix games and higher-order $n$-player strategic interactions. The Data Logger retains granular state–action–payoff histories, while the Results Analyzer computes empirical descriptive statistics, divergence metrics (e.g., Kullback–Leibler, Total Variation, Wasserstein distances), and benchmarks against theoretical solution concepts (Nash equilibrium, mixed strategies).

Pipeline summary:

Module	Purpose	Input/Output
Game Definition	Game structure, agent params	JSON config
Prompt Template	Instantiates natural prompts	Template per language
Agent Manager	LLM backend, personality	LLM API calls
Simulation Engine	Repeated play, logging	State/action/payoff logs
Results Analyzer	Statistical/game-theoretic	Summary stats, divergences

FAIRGAME’s modularity accommodates new game types, personality styles, language framings, and communication protocols without changes to core infrastructure (Buscemi et al., 19 Apr 2025, Buscemi et al., 30 Jul 2025).

2. Formal Game-Theoretic and Experimental Foundations

FAIRGAME implements finite, repeated normal-form games with the following elements: player set $N=\{1,\ldots,n\}$, strategy sets $S_i$, and payoff functions $u_i: S_1\times\cdots\times S_n \to \mathbb{R}$. For repeated games of horizon $T$, strategies can condition on the full public or private history. Solution concepts include Nash equilibrium and empirically observed behavioral distributions.

Key environments include:

• Prisoner’s Dilemma (PD): Actions $C$/$D$; canonical payoffs $T>R>P>S$.
• Payoff-Scaled PD: Multiplicative scaling $T(\lambda), R(\lambda), P(\lambda), S(\lambda)$ with $\lambda\in\{0.1,1.0,10.0\}$, fixing the ordinal structure to isolate incentive sensitivity (Huynh et al., 8 Dec 2025).
• Multi-Agent Public Goods Game (PGG): $n=3$ agents, each endowed with $e_t = c$, choose to contribute ($s_{i,t}=1$) or withhold ($s_{i,t}=0$). Payoff for agent $i$ at round $t$:

$$\pi_{i,t} = \frac{r \cdot \sum_j s_{j,t} c}{n} - s_{i,t} c,$$

where $r$ is the synergy factor.

FAIRGAME enables experimental manipulation of:

• Language (prompt translation, framing bias)
• Agent “personality” (injectable through system prompt)
• Knowledge (common vs. asymmetric reasoning, horizon effects)
• Communication (pre-move messaging)
• Incentive scaling (payoff magnitude)

Empirical outcomes include cooperation/defection rates, payoff trajectories, and divergence from theoretical predictions (Buscemi et al., 19 Apr 2025, Buscemi et al., 30 Jul 2025, Huynh et al., 8 Dec 2025).

3. Strategy Recognition and Behavioral Intention Inference

A distinguishing feature is FAIRGAME’s integration of supervised behavioral strategy recognition. Canonical repeated-game strategies—ALLC (Always Cooperate), ALLD (Always Defect), TFT (Tit-for-Tat), and WSLS (Win-Stay–Lose-Shift)—are encoded as label sequences, optionally perturbed with stochastic “execution noise” ($\epsilon \in \{0, 0.05\}$). Action–outcome pairs per round ($(\text{Outcome}_{t-1},\text{Action}_{t})$) feed into discriminative models:

• Logistic Regression and Random Forest (on flattened features)
• Feed-forward Neural Network (vector input)
• LSTM-based sequence model (preserves temporal context, most robust under noise, $\sim94\%$ accuracy at $\epsilon=0.05$)

These classifiers assign high-confidence ($p > 0.9$) labels to LLM play trajectories, enabling mapping between observable behavior and latent strategic intention (Huynh et al., 8 Dec 2025). This facilitates principled real-time auditing and early detection of undesirable strategies (e.g. exploitative free-riding).

4. Language, Personality, and Communication Effects

Systematic studies reveal robust cross-linguistic and interpersonal divergences in LLM agent behavior:

• Language: English framing consistently yields higher and more stable cooperation in both dyadic and group dilemmas (e.g., higher initial cooperation, slower decay in PGG). Vietnamese triggers faster end-game collapse and lower overall cooperation. Language-induced biases ("language-specific shift" $b_L$) rival or exceed architecture/model differences (Huynh et al., 8 Dec 2025, Buscemi et al., 30 Jul 2025).
• Personality: Injection of cooperative vs. selfish persona affects outcome distributions, though model-specific bias is not always fully overridden (e.g., Claude 3.5 Haiku maintains residual prosociality even when framed as selfish).
• Communication: Enabling messaging ("comm") increases cooperation in some models (e.g., Llama 4 Maverick, English/Arabic PD) but can decrease it or have mixed effects in others (e.g., GPT-4o), and strongly modulates message length, lexical adaptation, and trust signaling (Buscemi et al., 30 Jul 2025).
• End-game Effects: Both language and personality affect the sharpness and timing of end-game defection in finite-horizon repeated games; alignment instructions interact nontrivially with models’ priors.

Model-specific summary:

Model	Prosocial bias	Instruction adherence	Language sensitivity
Claude 3.5	Strong, high var.	Partial	Moderate
GPT-4o	High (coop), zero (selfish)	Perfect (selfish)	Extreme (coop)
Mistral Large	Moderate, stable	Strong	Low

Prompt language, process order, and role assignment should be randomized or controlled in AI governance to prevent implicit hierarchy or bias amplification (Huynh et al., 8 Dec 2025).

5. Applications, Implications, and Directions for AI Governance

FAIRGAME establishes a reproducible methodology for multi-faceted auditing, benchmarking, and bias recognition in agentic AI systems:

• Model selection for multi-agent deployment: Model-specific cooperation and variance profiles (including language and communication interaction) are strategic design choices for real-world systems.
• Governance and safety: Repeated-game auditing uncovers hidden framing, incentive, and role biases, informing governance in decentralized/competitive or collective settings.
• Early detection and intervention: Behavioral intention recognition supports real-time monitoring for emergent undesirable strategies (e.g. defection cascades, group exploitation), enabling timely corrective action.
• Cross-linguistic and primacy-effect management: Protocol-level randomization in prompt order and language is essential to avoid accidental hierarchies.

Limitations include the current focus on finite, repeated normal-form games (no support for extensive-form or stochastic games in production), static personality enforcement, and lack of in-simulation personality adaptation (Buscemi et al., 19 Apr 2025, Huynh et al., 8 Dec 2025). Future work includes the extension to more complex game forms, coalition formation, adaptive personality styles, and dynamic, learning-based template generation.

6. Relation to Other FAIRGAME Instantiations and Theoretical Underpinnings

Beyond LLM benchmarking, the FAIRGAME label also appears in other fair-ML and security protocol domains:

• Fair ML Auditing and RL Debiasing: “Fair Game” comprises an Auditor–Debiaser loop leveraging RL to minimize sequential fairness violation metrics (statistical parity, demographic parity, equalized odds, and predictive value parity) under distributional shift via constraint or penalty-based ERM (Basu et al., 8 Aug 2025). Auditor sampling can deliver order-of-magnitude gains in estimation complexity, while the RL perspective yields a dynamical view of social system convergence.
• Game-Based Security Protocol Verification: A parallel “FAIRGAME” variant formalizes fairness in distributed protocols using Strong Secure Equilibrium (SSE), providing tight coNP, D^P, and PSPACE decision procedures for protocol synthesis and verification under malicious rational coalitions (Brice et al., 29 May 2024). While sharing the emphasis on equilibrium and safety, this instantiation is not focused on LLM/AI agent benchmarking per se.

These extensions reflect the generality and flexibility of the FAIRGAME paradigm, solidifying its position as a foundational toolset for empirical, theoretical, and regulatory research in multi-agent AI and socially embedded autonomous systems.