LLM Strategic Reasoning: Agentic Study through Behavioral Game Theory

What does it truly mean for a language model to “reason” strategically, and can scaling up alone guarantee intelligent, context-aware decisions? Strategic decision-making requires adaptive reasoning, where agents anticipate and respond to others’ actions under uncertainty. Yet, most evaluations of large language models (LLMs) for strategic decision-making often rely heavily on Nash Equilibrium (NE) benchmarks, overlook reasoning depth, and fail to reveal the mechanisms behind model behavior. To address this gap, we introduce a behavioral game theoretic evaluation framework that disentangles intrinsic reasoning from contextual influence. Using this framework, we evaluate 22 state-of-the-art LLMs across diverse strategic scenarios. We find models like GPT-o3-mini, GPT-o1, and DeepSeek-R1 lead in reasoning depth. Through thinking chain analysis, we identify distinct reasoning styles—such as maximin or belief-based strategies—and show that longer reasoning chains do not consistently yield better decisions. Furthermore, embedding demographic personas reveals context-sensitive shifts: some models (e.g., GPT-4o, Claude-3-Opus) improve when assigned female identities, while others (e.g., Gemini 2.0) show diminished reasoning under minority sexuality personas. These findings underscore that technical sophistication alone is insufficient; alignment with ethical standards, human expectations, and situational nuance is essential for the responsible deployment of LLMs in interactive settings.

The rapid development of large language models (LLMs) and generative AI has significantly broadened their applications, transitioning from basic text generation [41] and completion tasks to serving as sophisticated agents [45, 60, 21, 17]. While existing benchmarks primarily assess LLMs on isolated language or math tasks [33, 23, 58], real-world deployment often demands more complex forms of decision-making, particularly strategic reasoning, where agents must interact with other entities whose actions directly influence the outcomes [64, 31, 22]. Specifically, one-shot strategic reasoning refers to an agent’s ability to select a single, irreversible action where the outcome depends on both its own choice and that of other agents in this interaction. Consider an AI agent operating in a business environment where strategic interaction is critical. In procurement, for instance, it must anticipate supplier counteroffers when negotiating orders; in advertisement bidding, it predicts competitors’ bids to set optimal prices. In each case, the agent faces a one-shot decision that directly impacts its payoff and cannot be revised post-execution [43, 12].

Related Literature and Research Gap. Research on LLM decision-making typically begins by examining their behavior as independent decision-makers [4, 11, 34, 16]. From an economic perspective, LLMs exhibit human-like patterns in preferences under uncertainty and risk [40]. In social science, they have demonstrated alignment with human responses in moral judgment and fairness related tasks [15, 39, 52]. Other studies further reveal alignments between LLMs and human judgments across diverse decision contexts [34, 46, 40]. However, when demographic profiles are embedded into prompts, systematic inconsistencies and fairness concerns emerge [29, 40].

Strategic decision-making extends individual reasoning into interactive contexts, where outcomes depend not only on one’s own choices but also on the anticipated actions of others. Existing evaluations of LLM strategic reasoning are predominantly grounded in game theory. Several studies explore LLMs’ abilities in achieving rationality within game-theoretic frameworks, such as mixed strategy Nash Equilibrium (NE) games [53] and classic strategic games like the prisoner’s dilemma [5, 28]. Some works investigate the adaptability of LLMs to various prompts that influence cooperative and competitive behavior [50], and others evaluate their capacity to replicate human-like reasoning patterns in multi-agent settings [1, 61]. While these studies provide a good starting point, many are limited to binary assessments of whether or not LLMs meet NE [35, 18] without quantifying their strategic reasoning capabilities or exploring the underlying mechanisms. While NE is a cornerstone concept in evaluating rational behavior, evaluating solely whether LLMs can achieve NE is an incomplete assessment of their reasoning capabilities [36, 32]. The primary limitation of using NE as a measurement lies in its strict assumptions and focus on outcomes rather than the decision-making processes [3]. It makes it difficult to interpret why LLMs deviate from optimal strategies. Also, NE assumes perfect rationality, which fails to account for the variability and bounded reasoning capability inherent in real-world problems. For LLMs—probabilistic models trained on human-generated data—this assumption is particularly problematic [63, 42]. Their stochastic nature makes NE impractical as a comprehensive evaluation metric, and its assumption of perfect rationality falls into the circular reasoning fallacy when assessing LLMs’ rationality. Recent work begins to address these issues by incorporating stepwise evaluation [19] or applying models like Cognitive Hierarchy (CH) [65], but these approaches still rely on deterministic assumptions about context and agent type.

Table 3 presents the reasoning depths evaluated through the framework for each model across games. Among all models, GPT-o1, GPT-o3-mini, and DeepSeek-R1 outperform others, with GPT-o1 ranking first in 6 games, GPT-o3-mini leading in 7 games, and DeepSeek-R1 securing the top position in 5 games. Some games have co-leaders, where multiple models achieve the highest evaluated strategic reasoning level. In these cases, certain LLMs consistently select strategies that align with theoretically robust principles while also demonstrating accurate anticipation of the opponent’s behavior. However, not all models achieve this level of capability, indicating variations in reasoning depth. This shows both the strengths of top models in structured settings and the effectiveness of our framework in distinguishing optimal decision-making from suboptimal or inconsistent reasoning. Additionally, our findings reveal significant variations in reasoning capabilities across different game types.

GPT-o1 consistently ranks among the top models in competitive and incomplete-information games, indicating a strong capacity for goal-oriented and adversarial reasoning. DeepSeek-R1 excels in cooperative and mixed-motive settings, likely due to its reinforcement learning-based optimization for social interaction and mutual benefit. GPT-o3-mini performs robustly across all game types, particularly in cooperative, mixed-motive, and incomplete-information scenarios, reflecting a balanced ability to manage trade-offs, adapt to uncertainty, and apply probabilistic inference.

We gather available internal or summarized reasoning traces from each model and link them with its observed behavioral choices. For each model–game pair, we extract the empirical strategy distribution from 30 independent trials and identify the dominant or mixed-strategy pattern. We then examine the corresponding reasoning traces through qualitative analysis, aligning textual reasoning steps with revealed strategic behavior to evaluate coherence between what the model says and what it does. To ensure robustness and mitigate subjectivity, we collect a diverse set of reasoning traces from different models and anonymize them before analysis. Researchers who coded each CoT trace for reasoning style did so without knowing which model produced it, following a “blind review” procedure that minimizes post-hoc bias. A pre-defined structured coding rubric was used to classify reasoning styles (e.g., maximin, belief-based anticipation, opponent-oriented logic), and cross-validation was performed by having multiple researchers independently code overlapping subsets and compare results for consistency. Finally, we record the completion tokens required by each model to quantify computational demand and analyze whether longer reasoning chains correspond to improved or diminished decision quality.

GPT-o1 consistently applies minimax reasoning, evaluating each option by its worst-case outcome. In nearly every reasoning chain we extracted, the model explicitly states, “I will now use minimax to help me make a decision.” This leads to strong performance in competitive games, where minimizing potential losses aligns with an optimal strategy. However, the same strategy becomes overly cautious in cooperative or mixed-motive games, where achieving mutual benefit often requires trust and risk-taking. GPT-o1 also exhibits a highly defensive stance, at times assuming that the opponent’s objective is to minimize its payoff, interpreting interactions as fully adversarial. GPT-o3-mini demonstrates greater flexibility. It primarily engages in belief-based anticipation, attempting to infer the opponent’s likely move and respond accordingly. This allows it to perform well in cooperative and mixed-motive settings, where alignment with the other player is key. Yet under uncertainty, GPT-o3-mini sometimes falls back to the worst-case logic, which can limit its potential in competitive games but also protects against major failures. DeepSeek-R1 adopts a strategy that begins with assumptions about the opponent’s likely action, typically based on the idea that the opponent will pursue their own payoff. This logic works well in cooperative games, where the players’ incentives are aligned, but lacks the adversarial caution required in competitive games. R1 also tends to exhibit strategic trust, assuming that when mutual benefit is unavailable, the opponent will not deviate simply to harm the other player, in contrast to GPT-o1, which at times assumes spiteful intent.

An additional observation relates to token usage, as shown in Appendix B Table 8. Contrary to intuitive expectations, higher token counts in internal reasoning do not correlate with better reasoning. In fact, GPT-o1 and DeepSeek-R1 are leaders in competitive and cooperative games, respectively, while they produce the shortest CoT outputs within their strongest games. We observe that longer reasoning chains often suggest hesitation and uncertainty, rather than deeper insight. Conversely, more concise CoT responses tend to signal higher confidence and more direct strategy choices. Notably, in competitive games, DeepSeek-R1 often exhibits repeated self-doubt in its CoT, but this results in redundant reasoning loops that inflate token usage without improvement. This points to future research on improving token efficiency in CoT generation, such as incorporating RL-based training that encourages decisive and diverse reasoning over repetitive patterns.

4.3 Effect of CoT Prompting

Our empirical study of top-performing models with embedded internal CoT reasoning motivates us to explore whether CoT prompting can also enhance models that do not natively generate internal reasoning. The strategic reasoning level after explicitly adding the CoT prompt is presented in Appendix B Table 9. Intuitively, many believe CoT can likely enhance a model’s reasoning ability. However, our results show that CoT’s impact on strategic reasoning is mixed, with no consistent improvement across all models and game types, which is consistent with prior findings suggesting that the "CoT does not always help" [18, 10], particularly in strategic settings.

A consistent pattern emerges around gender: when prompted with a “female” persona, several large models—such as GPT-4o, InternLM V2, and Claude 3-Opus—exhibit increased reasoning depth, suggesting deeper multi-level reasoning under female identity framing. Sexuality-based variation reveals further heterogeneity.

Mechanism note. Observed persona-induced shifts likely stem from statistical associations in training corpora that link demographic descriptors to behavioral patterns, potentially modulated by reinforcement learning from human feedback (RLHF). Models often deny explicit bias yet reveal implicit adaptation under identical payoffs, indicating latent contextual priors. Our framework surfaces these implicit shifts and quantifies their magnitude for downstream auditing and fairness alignment.