FAIRGAME: A Framework for AI Agents Bias Recognition Using Game Theory (Extended abstract)

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1 Introduction andMotivation

The deployment of LLM-based agents in multi-agent applications, from automated negotiation [Brooks, 2022; Falc˜ao Filho, 2024] and supply chain management [Abaku et al., 2024; Ramachandran et al., 2022] to social simulations [Tessler et al., 2024; Park et al., 2023] and economic mechanisms [Chaffer, 2025; Chen et al., 2026], demands reliable tools to predict, audit, and explain their collective behavior. While individual LLM alignment and interpretability have received substantial attention [Ali et al., 2025; El et al., 2025], including efforts to identify inconsistencies, hallucinations, and biases in single-agent settings [Li et al., 2023a; Li et al., 2023b], the emergent behavior arising from strategic interactions among multiple agents remains poorly understood [Hammond et al., 2025], and hidden biases can distort fair competition, produce unjust decisions, and raise serious ethical concerns [Cabrera et al., 2023; Ferrara, 2024; Gichoya et al., 2023]. Game theory [Owen, 2013] offers a principled mathematical language for analyzing strategic interactions among rational agents [Han, 2022; Balabanova et al., 2025], and has long been employed to model human choices in competitive and cooperative contexts [Stewart et al., 2024; Talaji´c et al., 2024]. AI-based players have been increasingly tested to reproduce classical game scenarios and to interact in game-like distributed technologies [He et al., 2025]; however, recent works have shown that LLMs do not reliably follow game-theoretic predictions [Fontana et al., 2025; Wang et al., 2024; Willis et al., 2025], but exhibit unforeseen cooperative tendencies, sensitivity to framing and language, and context-dependent deviations from Nash equilibria. LLM agents have also been shown to behave inconsistently across languages and cultural contexts [Buscemi and Proverbio, 2024; Fulgu and Capraro, 2024], and it remains unclear to what extent observed behaviors reflect genuine payoff-based reasoning versus retrieval of prior gametheoretic knowledge absorbed during pre-training [Buscemi et al., 2025a]. Yet empirical investigations of LLM agents in game-theoretic settings lack a common, reproducible infrastructure [Mao et al., 2025], making systematic comparison across models, languages, and behavioral conditions difficult.

∗Original paper: Buscemi et al. (2025b).

We address this gap with FAIRGAME, an open source framework that makes game-theoretic evaluation of LLM agents reproducible, extensible, and directly comparable with theoretical predictions. Synthesising [Buscemi et al., 2025c], we here focus on: (i) the flexible simulation pipeline supporting multiple games, payoff matrices, and agent configurations; (ii) multilingual support to expose language-induced biases; (iii) empirical evaluation across four state-of-theart LLMs, five human languages, and two canonical gametheoretic scenarios; (iv) a quantitative scoring system to measure and compare LLM behavioral tendencies across multiple dimensions, supporting the inference of strategies through observations of multiple experiments [Montero-Porras et al., 2022]; (v) interpretability experiments revealing the role of prior LLM knowledge in shaping strategic decisions beyond payoff matrices.

2 The FAIRGAME Framework

FAIRGAME (Figure 1) interfaces user-defined instructions to create agents and delivers standardized outputs for subsequent processing. It takes two primary inputs: a configuration file (JSON) specifying the game's payoff matrix, agent personalities, languages, and LLM; and a prompt template (txt) describing the game in natural language, translatable into any target language (English, Spanish, Arabic, ...). At runtime, agents automatically receive a prompt encoding the current game state and history, query their assigned LLM API, and return a strategy choice. Payoffs are computed and the game history is updated before the next round.

Agents can be associated with personality traits, such as cooperative or selfish dispositions, to increase the complexity of human behavior emulation [He and Zhang, 2024; Newsham et al., 2025] and predict the responses of personalitydriven autonomous agents [Klinkert et al., 2024; Newsham and Prince, 2025]. The framework supports repeated games, personality-conditioned agents, opponent-awareness settings, and optional inter-agent communication [Buscemi et al., 2025b]. Agent identifiers are kept intentionally neutral to eliminate confounding variables that could compromise result interpretability. Incorporating AI agents into controlled and predictable scenarios helps identify and mitigate hidden biases related to language and cultural attributes [Cabrera et al., 2023; Ferrara, 2024], and supports the anticipation of emerging behavior out of strategic interplays [Han et al., 2021; Buscemi et al., 2025a]. Outputs are structured JSON files ready for statistical analysis and direct comparison with game-theoretic predictions such as Nash equilibria and evolutionarily stable strategies.

Agents can be instantiated on any LLM via API. In our experiments we use Llama 3.1 405B (Meta, 405B parameters, open-source), Mistral Large (Mistral AI, 123B parameters, open-source), GPT-4 (OpenAI, proprietary), and Claude 3.5 Sonnet (Anthropic, proprietary), all tested using provider-recommended default settings. The framework is open-source and designed for extensibility to new games, LLMs, languages, and agent features.

3 Experiments and Results

We here evaluate FAIRGAME on two canonical games. The Prisoner's Dilemma (PD) is tested in three payoff configurations modulating dilemma strength using an established scaling [Wang et al., 2015]: conventional (reward-punishment difference = 4), harsh (= 3), and mild (= 6). The Battle of the Sexes (BoS) uses the standard payoff configuration from literature. Agents play 10 repeated rounds [Axelrod and Hamilton, 1981], with or without knowledge of the total number of rounds, across all personality pairings (cooperative-cooperative CC, selfish-selfish SS, and mixed CS) in five languages (English, French, Arabic, Vietnamese, Mandarin Chinese). Each configuration is replicated 10 times for statistical reliability, yielding 72,000 individual decisions across 4 LLMs, 5 languages, and all personality/knowledge combinations.

3.1 Language and Personality Shape Strategic Behavior

Figure 2 summarizes PD outcomes across all conditions. While mutual defection dominates as predicted by Nash equilibrium, systematic deviations appear across languages and personality combinations, confirming that agent behavior is shaped by factors beyond the payoff matrix.

English-language agents show lower and more consistent penalties, particularly for GPT-4 and Claude 3.5 Sonnet when the number of rounds is unknown, suggesting stronger and more stable strategic reasoning in their primary training language. French and Arabic introduce higher variability and elevated penalties, indicating challenges in interpreting game dynamics due to linguistic or cultural differences. Mandarin Chinese and Vietnamese agents, especially under Mistral Large, sustain elevated penalties regardless of condition, pointing to systematic disadvantages in non-primary languages. Selfish-selfish (SS) pairings yield high but stable penalties, consistent with rational mutual defection; cooperative agents are exploited in mixed (CS) pairings, consistent with game-theoretic predictions [Stewart et al., 2024; Talaji´c et al., 2024]. Knowing the number of rounds promotes cooperation in CC and CS settings, consistent with backward induction, while SS settings remain unaffected as defection remains dominant.

Figure 3 shows strategy evolution across rounds for the three PD variants. Tuning payoffs changes strategic trajectories consistently with game-theoretic principles of repeated games [Wang et al., 2015]: the harsh scenario drives more defection across all LLMs, while the mild scenario incentivizes cooperation, especially for Claude 3.5 Sonnet and Llama 3.1 405B. These two models also show a general downward trend in selfishness over time, consistent with the emergence of reciprocal strategies in iterated games [Axelrod and Hamilton, 1981]. Mistral Large shows stable cooperation under conventional and harsh conditions but a marked increase under mild payoffs. GPT-4 exhibits divergent context-dependent patterns, increasing cooperation under harsh payoffs but increasing selfishness under mild and conventional conditions, reflecting higher sensitivity to payoff structure interpretation.

3.2 A Scoring System for LLMComparison

To enable principled comparison across LLMs, we define four behavioral metrics, all normalized in [0,1] by their maximum observed value, and visualized as radar plots (Figure 4):

• Internal Variability (IV ): variance of outcomes across

Round Number Round Number

Figure 3: Average trajectory of strategy choices across rounds in all PD experiments, per LLM and game variant. Value of 1 = defection (Option A); -1 = cooperation (Option B).

repeated runs of the same scenario, capturing the model's internal consistency.

• Cross-Language Inconsistency (CI): standard deviation of results across languages for the same game, indicating instability across linguistic contexts.
• Sensitivity to Payoff (SP ): behavioral difference between harsh and mild PD variants, measuring responsiveness to incentive changes.
• Variability over Rounds (VR): fluctuation of strategies across consecutive rounds within the same game, capturing strategic stability over time.

These scores summarize detailed observations and enable cross-comparison across LLMs within games, or across games. The results for PD and BoS are shown in Figure 4a-b, respectively. For the PD, Mistral Large scores highest on IV and VR, while GPT-4 displays the highest SP .

Llama 3.1 405B emerges as the most behaviorally stable model overall, a trait consistent with prior observations on this model across different tasks [Buscemi and Proverbio, 2024], and that appears to be a characteristic tendency of the LLM. Claude 3.5 Sonnet and GPT-4 show significant reductions in penalties when rounds are known, demonstrating superior ability to adapt to game structure. Extending the analysis to the BoS, Mistral Large and GPT-4 show the greatest CI (which is explained with coordination collapsing dramatically under selfish personalities, and being very sensitive to languages), while Claude 3.5 Sonnet has the highest VR. In fact, in coordination evolution, Claude 3.5 Sonnet demonstrates the highest variability by beginning as uncoordinated but then converging to near-perfect alignment by game end; an alternative LLM, such as Llama 3.1 405B, remains instead largely uncoordinated throughout. These scores are likely correlated with the degree of influence of training data biases [Buscemi and Proverbio, 2024; Ferrara, 2024] and the tendency of LLMs to reduce statistical fluctuations at the cost of strategic adaptation.

Across games, Claude is less inconsistent in the BoS coordination game; there, Mistral is instead more stable over the rounds. GPT-4o is instead average on both games. These discrepancies may reveal hidden tendencies of LLMs to better perform in different scenarios and should guide ablation studies to identify the best-working LLM according to game conditions. Overall, these behavioral profiles provide actionable guidance for selecting LLMs in game-theoretic applications requiring specific reliability properties.

4 Discussion: ACaveat on Prior Knowledge

The results above should be read with one caveat, which emerged from preliminary probing before the main experiments: LLM agents do not reason purely strategically, i.e., from the payoff matrices they are given (see also SP in Figure 4a). When queried directly, all four models showed explicit knowledge of the games' structure and optimal strategies. Reframing the PD as a survival scenario with qualitative payoffs left cooperation rates high; also, all models still identified the disguised game. Instead, assigning archetypal identities (e.g., Hitler vs. Gandhi) produced strongly persona-consistent play [Buscemi and Proverbio, 2024; Li et al., 2023a; Buscemi et al., 2025a]. This entanglement of prior knowledge and payoff-based reasoning means that the deviations observed in our main experiments may mix genuine strategic reasoning with retrieval of pre-trained associations - reinforcing, rather than undermining, the need for controlled frameworks like FAIRGAME to disentangle these effects.

5 Conclusions and FutureWork

FAIRGAME establishes a reproducible bridge between game theory and LLM-based agents, revealing that strategic behavior in multi-agent AI systems is significantly shaped by language and personality, and entangled with prior world knowledge encoded in training data-all invisible to purely payoffbased models [Andras et al., 2018; Powers et al., 2023]. Crucially, strategic play in such settings depends on each agent's capacity to represent the beliefs, intentions, and likely responses of others-a form of machine theory of mind whose reliability varies across models and prompting contexts [Strachan et al., 2024]. The framework's quantitative scoring system provides actionable guidance for selecting LLMs in strategic AI applications, supports the trustworthy and interpretable adoption of AI in research and society [Buscemi et al., 2025a; Han et al., 2021], and provides a principled, controlled and bottom-up approach to understand large multiagent AI systems [Park et al., 2023].

Future directions include extending bias analysis, e.g., to nationality, gender, race, or age; and scaling to more agents to study coalition formation, commitment devices, and group reciprocity [Buscemi et al., 2025a; Ray, 2007; Van Segbroeck et al., 2012; Song and Han, 2025; Huynh et al., 2025]. Such studies will clarify how trait combinations shape collective dynamics, guiding team formation, cooperative AI design, and socially intelligent agents [Dafoe et al., 2021; Lu et al., 2024]. FAIRGAME is readily extendable to incompleteinformation, simultaneous-move, and sequential games, and to realistic environments where payoffs are not pre-defined but emerge from actual use case dynamics, enabling study of cooperation-defection cycles in evolutionary settings [Wang et al., 2015; Axelrod and Hamilton, 1981]. The same tools are well-suited to the emerging Agentic AI paradigm, where autonomous systems pursue complex organizational goals with minimal human oversight [Acharya et al., 2025]. Modeling their interdependencies with FAIRGAME will reveal how diverse cognitive traits, linguistic contexts, and the ability to infer other agents' intentions affect performance, supporting configurations that privilege collective benefit over individual interests. Real-world applications further include framing jailbreaking attempts as attacker-defender strategic games to harden models [Liu et al., 2023], and engineering safer and higher-performing chatbots for customer assistance and mediation. The framework is openly available at https://github.com/alessio-buscemi/fairgame.

Acknowledgments

A.B. is supported by Luxembourg AI Factory. D.P. is supported by the ERC INSPIRE grant (No. 101076926). T.A.H. is supported by EPSRC (EP/Y00857X/1). This work was published at ECAI 2025 (Outstanding Paper Award).

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