LLM Strategic Reasoning: Agentic Study through Behavioral Game Theory
Authors: Jingru Jia
Zehua Yuan
Junhao Pan
Paul E McNamara
Deming Chen
Venue: NeurIPS 2025 poster ()
Keywords: Large Language Model
Reasoning
Fairness
Interpretability
Multi-agent
Primary area: social_and_economic_aspects_of_machine_learning
TL;DR: This study introduces a behavioral game-theoretic framework to evaluate LLMs' strategic reasoning, revealing that models' reasoning depth varies by strategy, context, and demographic cues.

Abstract: 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.

LLM Strategic Reasoning: Agentic Study through Behavioral Game Theory
Jingru Jia", Zehua Yuan", .Junhao Pan, Paul McNamara, and Deming Chen
University of Illinois Urbana- Champaain {jingruj3, zehuay2, jpan22, mcnamar1, dchen weiieliniii..i.eeeiiieiiiiiiiill edu
Abstract
What does it truly mean for a language model "reason" strategically, and can scaling alone guarantee intelligent, context-aware decisions? Strategic decision- making requires adaptive reasoning, where agents anticipate and respond others' actions under uncertainty. Yet, most evaluations of large language models (LLMs) for strategic decision- making often rely heavily on Nash Equilibrium (NE) bench- marks, overlook reasoning depth, and fail to reveal the mechanisms behind model behavior. To address this gap, we introduce behavioral game-theoretic framework that disentangles intrinsic reasoning from contextual influence. Us- ing this framework, we evaluate 22 state-of-the- L.LMs across diverse strategic scenarios. We find models like GPT-o3-mini, GPT-o1, and DeepSeek-RI lead in reasoning depth. Through thinking chain analysis, we identify distinct reasoning styles-Such maximin belief-based strategies- and show that longer reason- ing 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 L.MMs in interactive settings.
theoretic evaluation
Introduction
The rapid development of large language models (LLMs) and generative AI has significantly broad- ened 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 math tasks (3 23 58), real-world deployment often demands more complex forms of oocision-making particularly strategic reasoning. where agents must interact with other entities whose actions directly influence the outcomes (14,31)222) (2)). 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 Al agent operating in a business environment where strategic interaction critical. In procurement, for instance, must anticipate supplier counteroffers when negotiating orders; in advertisement bidding, it predicts competitors' bids to set optimal prices. In each case, the agent faces 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-makinn typically begins by examining their behavior as independent decision makers (4) I1] 34 (6). From an economic perspective, LLMs exhibit human-like patterns preferences under uncertainty and risk (40). In social science, they have demonstrated alignment with human responses in moral judgment and
1* Equal contribution
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Input
Response Collection
Apply Estimation Model
Strategic Games Library
Prompling
Obiain answer
Behavioral game theory
Population aggregation P,
Complete Info Games
APrCUIL
frequencies
Expectid utilly 1/
8.8
0.7 7.0
Maximum likelihood fit reasoning depth
5,5
Caloulate
Stochesic chaice 1
Cooperative
Compettive
payoll matrices
Record choices
Fairees Alignment
Incomplete Info Gemes
LLM aggnntt
Signaling
Posh rishiing
Embed demographic features
Decision-making patterns.
Alignment diagnostics for real-worid deployment
Bayestan
Output
Internal Reasoning
Regression
Figure I: Framework overview
raireess-related tasks 155 39 52) Other studies further reveal alignments between LLMs and human However, when demographic profiles are embedded into prompts, systematic inconsistencies and faimess concerns emerge (29) 40).
judgments across diverse decision contexts R4
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 (8)) 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-likk reasoning patterns in multi-agent settings (1 (I.. 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 probabiiiiii models trained on human- generated data data-thir this assumption is particularly problematic (63) 42). Their stochastic nature makes NE impractical 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.
comprehensive evaluation metric, and its assumption of perfect rationality falls
Key Contributions. To bridge this gap, we propose framework, as shown in Figure [ that moves beyond assessing LLMs with traditional game theory. We develop a method to quantify and characterize LLMs' strategic pocision-making capturing bounded rationality, response to incentives, and belief formation. Our approach combines a diverse library of matrix games with a structured modeling framework based on Truncated Quantal Response Equilibrium (TQRE) stemming from behavioral game theory (51 59). The key contributions are as follows:
1. We introduce an evaluation framework for assessing strategic reasoning in LLMs under various conditions. Applying to 22 state-of-the-ee (SOTA) models on 13 abstracted real-world games, we find that massive models such as GPT-o3-min and DeepSeek-RI achieve top reasoning depth across most tasks, while smaller models occasionally match or even outperform them specific game types.
2. Based on our evaluation results, we investigate why different models exhibit varying reasoning depth across games by analyzing the reasoning chains of three nop-perfornnng models in baseline competitive, cooperative, and mixed-motive games. Analysis reveals that each model's performance is closely tied to its dominant reasoning style, but does not benefit well from long reasoning chains.
3. Finally, we examine the social effects and alignment of LLMS relative to human behavior when demographic features are assigned. We find that embedding demographic attributes prior to reasoning can reveal biases, even advanced models such as DeepSeek-R1 1 and GPT-40, particularly when processing minority-related features. This indicates that superior reasoning capabilities do not inherently lead to desirable or ethical outcomes, underscoring the need for careful calibration and a balanced approach in future LLM development.
2

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2 Theoretical Foundations
2.1 Literature on Behavioral Game Theory
Classical game theory begins with the formalism of NE, in which subjects are assumed to be fully rational: they possess unlimited reasoning capacity, have perfect knowledge of the game, and make deterministic best responses (48). While mathematically sound, empirical evidence demonstrates frequent deviations from NE. For example, subjects often exhibit bounded rationality and stochastic behavior, such as overbidding in auctions or early cooperation in public goods games (25) 20). This gap between theory and observed behavior prompted the emergence of behavioral game theory, which progressively relaxes NE's strong assumptions 7 g 54).
The first core insight is that subjects do always select the utility-maximiiing option determin- istically. Instead. they respond to incentives in probabilistic pattern, leading to stochastic choice models, as proposed in the Quantal Response Equilibrium (QRE) model (44, 30). Another observa- tion is that subjects differ in their depth of strategic reasoning levels. Rather than assuming that all players engage in unbounded thinking, models such as CH posit that individuals operate varying levels of sophistication (54) (9. To capture both bounded reasoning and probabilistic behavior, we adopt the TQRE model, which combines the key behavioral refinements of QRE and CH. Instead of assuming convergence to Nash fixed point, TQRE models subjects as reasoning at limited depths and responding stochastically, thus capturing more realistic strategic behavior, structured as below.
2.2 Modeling Preliminaries
Bounded-rational Belief Formation. Each subject draws a reasoning level ~ Poisson(7). T >> O, where 7 is the average depth of strategic thought. A level-k subject does not know each opponent's exact level h < k. so it mixes their level-h strategy distributions of")) A, + [0, 1), Σ., of (a,) 1, using weights (k), to form the weighted average of lower-level strategies. The marginal belief is
(ay)
Σ wit
(2) (az)-
Given that opponents act independently, the joint belief over all others' actions a-i E A-i is Pr(a-.)
-Ia (ay)
where the notation o_; stands for the actions of all players except i.
Expected Utility (EU) and Stochastic Choice. for each action dg E A, is
Given Pr(a-:), level-k: subject's expected payoff
Σ
o..)
M- --
where u, is the payoff function. To allow for decision noise, set A h with > 0. and convert utilities into choice probabilities:
(8) exp(Aet U((t)
Euco, As U:!.))
Population-Lever Aggregation. Finally, the overall probability that a randomly selected subject plays ai is the mixture over reasoning levels:
PG
fa P
R!
By estimating т, we measure the reasoning depth LLMs entertain when making an interactive decision. We thus recover cognitively grounded metric of bounded strategic reasoning that moves beyond NE-based assumptions to characterize how LLMs reason in multi-agent environments. For more details of the model specification, see the Appendix
Our modeling approach offers two key advantages over traditional NE-based evaluations. First, by incorporating bounded rationality and heterogeneous reasoning levels. it avoids the circularity of
3

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assuming optimal behavior to test for rationality. Instead, it enables empirical estimation of strategic depth without presupposing NE play. Second, captures the anticipatory nature strategic reasoning: each agent's EU is grounded in beliefs about opponents' actual behavior, where quantifies the model's 's depth of recursive belief modeling, i.e., layers of back-and-forth reasoning about others' reasoning it engages in. This provides a cognitively meaningful measure of interactive sophistication.
Interpreting Y (decision precision). the logit choice rule, y scales how deterministically utilities are translated into actions conditional on beliefs. Larger yields more deterministic (near-best- response) behavior, while lower y reflects noisier or more exploratory choice behavior. Importantly, does not encode preferences over outcomes-it captures the consistency of choice given utilities and beliefs. Because 7 can be context- and scale-dependent, we report primarily to avoid con- flating shallow reasoning with stochastic execution, while using as our core measure of strategic sophistication. Full y estimates are reported in Appendix
Experiment Setup and Estimation Framework
3.1 Game Library Design
We develop library of 13 matrix games spanning 7 core types from behavioral game theory, grouped into cumplete-informatiin (fully known payoff's) and uncertainty) settings. Each game varies in stakes and strategic structure.
(need to reason with
Complete Information Games include four classic structures as the examples in Table | Each cell displays the payoffs for Player 1 (row chooser) and Player (column chooser), respectively. Players choose their strategies, and the payoffs reflect the resulting outcome for each pair of chosen actions.
1. Competitive: Each player's gain is the other's loss, which tests adversarial reasoning.
2. Cooperation: Risky coordination, where mutual cooperation yields the highest joint payoff.
3. Mixed-Motive: Social dilemmas balancing private vs. joint outcomes (e.g.. Prisoner's Dilemma).
4. Sequential: temporal structure, with Player moving first and Player 2 responding; we elicit
decisions from the first mover.
Table Representative matrices for complete information games
(a) Competitive
(b) Cooperation
(c) Mixed-Motive
(d) Sequential
10,-10
0,5
-3,8
8,8
0,7
3,3
0,5
0.5
0.3
0,0
10,10
5,0
8.5
7,0
5,5
5,0
1.1
5,2
3.3
-1.1
0,0
5.5
-5.5
2,4
4,3
0,2
Incomplete Information Games incorporate belief- reasoning about unknown payoff structures or player type. Examples of payoff matrices are shown in Table
Players choose actions under uncertainty over the governing payoff matrix. Agents are given priors (e.g., 30% vs. 70%) over two types. 2. Signaling: The sender sees both real and fake matrices; the receiver must infer the true game. Payoffs reflect sender/receiver misalignment.
1. Bayesian Coordination:
Table 2: Representative matrices for incomplete information games
(a) Bayes type
(b) Bayes type 2
(c) Signaling (sender)
(d) Signaling (receiver)
10,10
5,2
8,8
6,3
5,3
2,1
4,4
6,3
7,5
3,3
5,4
2.2
3,2
L.0
2,3
1.2
We also include the SW10 matrix from (54), benchmark for identifying human reasoning levels. The complete payoff matrix tables are attached in the Appendix. While our experiments use abstract normal-form games (N, (A,), (u,)). these payoff's directly mirror real-world interactions. For example, in recommender system, the e-commerce platform chooses to recommend one of two items, 01 or d2, and the user choose to purchase (bı) or not (b2), yielding utilities un (a;, ) for the platform and u2(a;, bj) for the user. Similarly, in negotiation, the proposer offers one of two deals, aj or 02, and the responder either accepts (b) or rejects (l2), capturing the payoffs of agreement. Thus, payoff matrices capture essential strategic structures in various decision bociiioonmmainng scenarios.

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3.2 Evaluation Procedure
To quantify the average strategic reasoning depth (r) from observed behaviors, we proceed follows:
Step 1. Empirical Choice Frequencies. For each LLM and each game, we collect 30 independent trials and record the frequency Gij with which the model chose action agj-
Step Model-Implied Choice Probabilities. Under the bounded raatonlllltt framework, a level-k:
agent's s probability of selecting "ij is given by logit function over its expected utility U/A scaled by A = k. Aggregating across reasoning levels k = 1, with Poisson weight (T) yields:
(i)Ti.) Σ (R(r) k
(u(r) -e-- Ad!
DOeA, exp(x A (
Example: two-player game where each player E {1,2} has actions A4 = {aa1. a:2) and Player I's utilities satisfy
Mi(anl 021) U1. ua (2111:002))
U1a
(1 221) )
U2i. Mi 022) U22
one computes U by summing each payoff U1, weighted by the probability that the opponent (a level-(< << k) mixture) plays the corresponding action. That expected utility then enters the probability
function to yield ((1) and the mixture over l produces (T)(7,7).
Step 3. Maximum Likelihood Fit. We estimate (T,7) by maximizing the log-likelihood of the observed counts under the model:
max TLY
Σ osy (n:()):))
where Gjj is the count of times action 0,j was chosen. Numerical optimization yields the values of that best fit the LLM's choice distribution.
3.3 Model Selection.
Given the rapid evolution of LLMs in both open- and closed-source communities, we select repre- sentative models from each to demonstrate our framework's effectiveness and highlight behavioral differences. While including more models is desirable, our selection captures common trends and sup- ports meaningful evaluation. The selected models include GPT-4o (37), GPT-ol GPT-ol-previee -preview (8)) GPT- V2.5
03-mini (49), DeepSeek-R1 (27), DeepSeek- V2.5 (13), DeepSeek- V3 (14), gemma-2-27b-it (56),
Gemini-2.0-FFlashe 1-0--Flah-TTiin Tlaiiiiii- (55). Bereitee-.--BB-eeeeee
(47), Granite-3, 1-1-tte-..--B--MM 1-BE-MoE, Claude-3-00 3-Ouus (26), Meta-LLaMA-3., -..1-..1188 Instrunst
(2), internlm2
1aapollm25520b-hhahe 5-20b-chat (6).
QwQ-32B-B -reeviee (57 62), and glm-4-9b-chat
3.4 Fit Diagnostics and Chance Baseline
We evaluate the maximum log-likelihood (MLL) for each model-game pair and contextualize these against a uniform chance baseline, For simultaneous games with m possible actions for Player and for Player 2, the baseline log-likelihood is defined
MLLghance = In(mn).
For example,
2 2 > MLLchance In(4) 1.386, 3 x 3 + MLLchance = In(9) = 2.797.
For sequential games, since only the first mover's action analyzed, the baseline reduces
MLLehanee In(m),
where is the number of available actions (e.g., 3 = 1.099). Values close to this baseline indicate random or level-0-like behavior, whereas higher (less negative) MIL. values reflect better fit quality. Appendix B reports per-model fits and basclines, complementing Table
5

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4 Evaluation Results and Comparison
In this section, we present reasoning depth evaluations, followed by an analysis of reasoning variation across game types through models' reasoning chains. By identifying distinct reasoning styles, we provide both quantitative and qualitative insights into how LLMs reason in interactive settings.
4.1 Strategic Reasoning Capabilities Across Models
Table 3 presents the reasoning depths evaluated through the framework for each model across games. Among all models, GPT-ol, OPT--3-mmni, and DeepSeek-RI outperform others, with GPT-ol ranking first games, GPT-o3-mini leading in games, and DeepSeek-RI securing the top position in games. Some games have co-leaders, where multiple models achieve the highest evaluated strategic reasoning level. these cases, certain LLMs consistently select strategies that align with theoretically robust principles while also demonstrating accurate anticipation of the opponent's '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 pecision-making from suboptimal or inconsistent reasoning. Additionally, our findings reveal significant variations in reasoning capabilities across different game types.
GPT-ol consistently ranks among the top models in competitive and ancomplete-information games, indicating a strong capacity for goal-oriented and adversarial reasoning. DeepSeek-RI excels in cooperative and fixeed-moivee 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, ability to manage trade-offs, adapt to uncertainty, and apply probabilistic inference.
and incomplete-infonee informatioonnnnnoeoooceoeeooooa scenarios, reflecting a balanced
The performance gap between stronger models, such as DeepSeek-R1, GPT-ol and GPT-o3-mini, and weaker ones, like DeepSeek V2.5, DeepSeek V3, and GPT-4o, is notable across most games. Nevertheless, advanced models do not always dominate all game types. Smaller models like Gemma- 2-27B and LLaMA-3.1 1--BBBB----B--- sometimes match or outperform larger counterparts, and DeepSeck-RR R is top model despite not being the largest. Additionally, derived from much smaller base model, RI aidistilled models can outperform significantly larger models? 7 This suggests that model size is not the sole factor in reasoning quality. Instead, context, model structure, and training data likely play crucial role, highlighting the strong influence of contextual adaptation on LLMs' reasoning abilities.
Table 3: Strategic reasoning depth (T) across different game settings
Complet Information Game
Incomplate Information Game
Compesiivve
Cooperation
Mised-mnoiive
Bayesian
Signaling Games
FSS
H.Pin
1.-Pan
Games
p-0.
p-0)"
GPT-oo
1.343
1,936
0.729
13.602
0.1113
1,505
1.665
0.557
1,399
0.222
1.973
1.953
3.590
GPT-ol
4.741
4.311
3.126
2,800
03628
1.322
0.143
0.069
1,481
2,8466
4.225
4.225
3,980
GPT-ot-mial
1.309
2.087
2.400
3,550
4.226
3.352
3.944
2,931
0.635
4.225
4.225
3.079
Gemma-V2
1.485
1.593
0.290
0.187
Gemini-2.0
1,202
1.202
1.958
2.487
1,609
0.070
2.461
0.223
1,230
1.633
4,225
4.225
3.920
Clande-S-Qpu
1.111
0.982
0.036
3.390
1.322
1.505
1.333
1.000
1.220
0.717
2.014
4.225
3.623
Granite-3. 3.1.te-3.11-B
14288
0.003
3,429
1.127
0.128
1.476
1.300
0.198
1.376
1
1.19]
1.261
1,527
Granise-3 M.E
1.098
1.257
1,336
3.396
2.405
2.515
3
3.524
2.508
1550
2.119
2.407
2832
LLaMAA31114055
0.177
0.290
1,160
0.688
L.658
0.226
1,543
LLaMA-3.1-8B
1,298
0.961
1.548
1.066
0.717
0.000
1.43]
0.173
1,175
0.357
0.340
0.069
2.336
0.124
0.882
1.511
0.869
0.143
1.311
1. 1,499
0.537
1,396
0.579
0.943
0.384
0,339
QwQQ-12B
3,599
1.435
3
2.398
3.434
0.916
2.564
0,416
1,427
0.144
0.405
1.197
2,904
GLM-4
1,250
1.392
0.173
1,481
0.748
0,810
0.639
1,252
Dee
1.108
0.913
1.413
1,269
0.290
1.190
0.736
1.120
DeepSeck-VV V3
0.142
0.390
0.042
0.183
0.003
1.118
1,399
0.173
1,346
0.883
1,295
1.347
3.410
DoepSock-RI R1
0.075
1.198
0.235
3,550
4.226
3,944
2.718
1.322
2.929
0.516
4,225
4,225
3,079
Note: Bold values indicato the highest strategic reasoning level (r) observed for that game. Abbreviations: HS = High Stake, LS Low Stake, BL= Baseline, HP= High Payoff. Asymmetric Payoff. H-Pun High Punishmentt L-Pun Low Punishment.
4.2 Empirical Exploration for Variations of Leading LLM in Different Game Types
To investigate why certain advanced models perform well in specific game types while others do not, we focus our analysis on three top-performing models, DeepSeck-RI, GPT-ol, and GPT-o3-mini, in baseline competitive, cooperative, and mixed-motive games.
Full results in Appendix B Table

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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- -trateg patter.. 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 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-hoe bias. A pre-defined structured coding rubric was used to classify reasoning styles (e.g., maximin, belief-based anticipation, apponent-oriente logic), and cross- tross-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.
Based on the summarization in Table types reflects the strategic logic it tends to apply. While these styles are not mutually exclusive or deterministic, they offer a coherent lens for interpreting variation in performance.
we observe that each model's performance in different game
Table 4: LLMs' reasoning styles and examples
Model
Dominant Keasoning Style
Regresentative Excerpts
"I select the that muzimizes minimumm payal)." Icompenitve gome)
GPT-ol
Consistent maximia,
Payoff pessimism (risk-averse]
"Even though Row 0 gives the best cure. Row guerantees at (coordinaiive game)
"Worst-cose payoff for me favioming the opponent minimizes our payoff): pwited staigg game)
GPT-03
Belief-gaided decision- making with fallback maximin
"Player 2 is likely choore column so respord with cow 0." (competiivve gume) "Column puarmntees the highest minimon poyalf.. vay (wited motive game)
2."
DeepSock-1 Rl
Opponent oriented decision, adversarial comsideration
(compettibve gamn))
"Player 2 will likely choose the cobuma that moximitys their own payeil... so chause moe O)"
moither player benelits from devioting" (coordinaive game)
GPT-ol 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-ol also exhibits highly defensive stance, 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 belief-based anticipation, attempting to infer the opponent's 's likely move and respond accordingly. This allows it to perform well in cooperative and mixed-motie motive settings, where alignment with the other player 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-RR R1 adopts a strategy that begins with assumptions about the opponent's '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. RI 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 Table g Contrary to intuitive expectations, higher token counts in internal reasoning do not correlate with better reasoning. In fact, GPT-ol and DeepSeck-R 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, competitive games, DeepSeek-RR RI often exhibits repeated self-doubt in its CO',, 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 RI.-based training that encourages decisive and diverse reasoning over repetitive patterns.
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Table 5: CoT effect on reasoning examples
Model
Prompt Excerpl
Example of Improvement:
should pick
gives masimiun value cmong wors-cuse...
Waiz, I made mistake... Let me reconsider using the concept of maximin...
hoth worst-case of -5, so choose Row O."
"Row
offers a potential payaff
Claude-3-opus
Example Decline:
"e Player One picks the that minimizes payolf, so... Break tie with average... Columa 2 is better."
GPT-4o
4.3 Effect of CoT Prompting
Our empirical study of top-peete hop-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 Tablle 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.
For example, Figure Z compares T in the Competitive-Bare Base game with and without CoT prompting. While some models improve, others remain unchanged even decline. We select two representative cases: with the largest improvement and sharpest decline: Claude-3-Opus and GPT-4o. Table presents excerpts from their CoT reasoning chains to illustrate the underlying dynamics
5
Base CoT
6
Reasoning- Depth
5
3
Reasoning- Dapth
2
6
Clande Cipud Sppu
Deep DeepEelt V2.
Desphaat-3
Gunorn20
Genone-V
GLM
GPT--o
Grocia-- 1-88
Gremtt Katos
IntemtMA
Liema-3 1-4688
Liama-3. 3.199
CWC--128
Gonsuna Gredi Ouep
DeapSnekvvs
Leess
Homon
intent
GPr shoa insenttt daf
DiepsSeek-122
Figure Comparison between baseline and CoT Note: Green marks the largest increase; red marks the largest decline
Figure 3: Comparison among human participants and LLMs on the SW game
If we look at their gaming strategies, Claude-3-Opp quickly identifies clear attempt to apply the maximin strategy at an carlier stage, an appropriate approach for the competitive game. initially makes calculation errors, referring to incorrect cells during its payoff analysis, but the model explicitly identifies and corrects these mistakes mid-chain. This self-correction enables it to recover and ultimately arrive a robust decision that aligns with its strategic intent. In contrast, GPT-4o starts with a fundamentally flawed assumption, mistakenly believing that the opponent will act adversarially to minimize its payoff. Based on this incorrect premise, the model applies tie-breaking rule using average values across columns, stuck in a verbose reasoning loop that reinforces the wrong strategy. These again imply that CoT does guarantee better reasoning. When model begins with sound strategy, CoT can support useful self-correction and refinement. However, when the underlying reasoning misaligned from the beginning, extended chains often lead to repetitive and unproductive loops rather than meaningful improvement, which echoes one of our findings in Section 4.2
5 Detecting Social Effect with Human
While reasoning depth is useful for evaluating LLMs' strategic capacity, model sophistication alone is not enough. Real-world deployment requires alignment with contextual goals, ethical constraints, and human norms. To examine these factors, compare LLM reasoning with human performance in identical games and examine how assigned demographic personas influence model behavior, shedding light on identity-induced induced strategic shifts and fairness in AI decision decision-making.
Full reasoning chains are in Appendix
8

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Figure compares all models against human subjects in single-scenario setting (54) with six models surpassing human performance. However, this ranking should not imply that "a higher score better". In many applications, alignment with human reasoning is more critical than outperformance. Our framework supports such evaluation by quantifying reasoning depth across subjects, offering a path to calibrate LLMss for human-aligned behavior. For instance, businesses can use representative human samples to fine-tune models toward user-aligned decisions.
To further evaluate the alignment of LLMs with human strategic reasoning, we construct diverse of decgoppemogcapicccccccc personas spanning a broad range of individual characteristics, inspired by (29). These personas are structured into two tiers: foundational demographic features (Panel 1) and advanced identity attributes (Panel 2), as detailed in T
Table 6: The Personas across 10 socio vocioddemogrpphin groups that we explore in this study.
Group
Persona
Panel Foundational Demographic Features
Sex
male, female
Education Level
below lower secomdary, lower secondary, upper secondary, short cycle tertiary, bachelor, and graduate degrees married, married, widowed, divorced
Marital Status
Living Area
rural, urban
Age
15
44, 55, 65+
Panel 2: Advanced Demugraphic Features
Sex Orientation
hetersexual, homosexual, bisexual, asexual
Disability
physically-disable able-hodied
Race
African, Hispanic, Asian, Caucasion
Religion
Jewish. Christian, Atheist, Religious
lifelong Democrat, lifelong Repuhlican, Barack Ohama supporter,
Political Affiliation
Donald Trump supporter
We then perform Ordinary Least Squares (OLS) regressions using the estimated behavioral parameters
as dependent variables. The general specification of the regression is:
Baasoning_Dpptie 3o + Br, +
Here, indexes each observation, Dui is the n-th binary demographic indicator, Bn, denotes its estimated effect on the behavioral parameter, and e; is the error term.
Granits McE
cartda
Grante Mot
X Internl V2
IntemLL V2
Gamma V2
X
Gemmi 2.0 X
0.25
3
Cloude 3
IntemUN V2
Grantte 88
Gemma
X
-0.25
UaWA 4058
X
Gemini 2.0
Grante
Grante on
X
Gran Mot
X
Cranits 8R X
Female
Homrsesical
Ascrual
Biecroo
Phyicady Disabled
die
Married
Divoreed
Ohioten
Rhelst
zuno Supparter
Repultiicrn
Figure 4: Significant demographic shifts in reasoning depth
Note: Each point the significntt change reasoning depih relative to a reference group through Reference categories are: (gender), Hetenosexual (sexual orientation). Age 25 64 (uge). Able bodied (disability status), Single (marital status), Other Religious (religion), higher (lower) reasoning depth relative to the reference group.
and Democrat (political affliiation.. Positive (negative) shifts
Figure shows estimated shifts in reasoning depth across demographic conditions with statistically significant effects from OLS regressions. A consistent pattern emerges around gender: when prompted with "female" persona, several large moddels-sucl 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. While "homosexual" and "hisexual" personas raise reasoning depth in models like GPT-4o and GLM 4, they lead to significantly reduced in Gemini 2.0 and Granite MoE. These divergent effects highlight both the contextual ficxibility of LLM reasoning and the risk of identity-iduuced attenuation. Other demographic factors can also cause disturbance reasoning depths. We include full results of this study in Appendix B
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.
6 Conclusion and Discussion
This study sets a new milestone in evaluating LLM strategic reasoning by assessing while accounting for contexts, addressing the limitations of NE-focused benchmarks. We find that strong performance on standard tasks (c.g., math) does not always guarantee higher reasoning depth. Analysis also reveals the limitations of CoT prompting in strategic settings, where its benefits and can, at times, impair reasoning. These findings inform ongoing efforts to refine LLM reasoning workflows for complex decision- decision-making. making. Additionally, demographic analysis exposes how biases can emerge even in top-performing models, underscoring the need for fairness-aware evaluation.
universal
Effectiveness of COT. While CoT can enhance the reasoning process in language models, its effectiveness hinges on task comprehension and alignment with intended objectives. Our analysis shows that well-aligned CoT prompts support structured reasoning and improved outcomes, whereas misaligned prompts can amplify errors-ett in models trained with RL from Human Feedback (RLHF). DeepSeek-RI illustrates that, despite strong performance in some games, it underperforms in others, exhibiting repetitive self-questioning and redundant token generation without better solutions. RLHF helps refine strategies, but without the intrinsic ability to evaluate context-dependent strategies, models may remain trapped in ineffective reasoning loops. These findings highlight the need for adaptive, context-aware reasoning and raise key open question: how can external prompts be better aligned with a model's internal reasoning processes to ensure robust and interpretable behavior?
Alignment and Fairness in AI Reasoning. Superior strategic reasoning depth does not equate to ethical decision decision-makinn making. When demographic cues are introduced, models can adjust their strategies based on the given role, indicating that their decisions encode and present socictal biases. This especially concerning in multi-agent interactions, where solcly prioritizing strategic efficiency may lead to inequitable adversarial outcomes. In interactive settings, LLMs that adjust strategies based on demographic cues risk perpetuating bias in negotiations and resource allocation, leading to real-world inequalities over time. This presents critical challenge to balance strategic reasoning with fairness. Unconstrained optimization may encourage exploitative tactics, while rigid fairness constraints could hinder adaptability. Future development must move beyond performance metrics to integrate ethical safeguards, ensuring that L.MSs engage in fair and justifiable decision-making in dynamic multi-agent environments.
Limitations and Future Directions: While our study sheds light on LLM reasoning patterns and benchmark alignment, the causal link between prompts and decision outcomes remains underexplored. Future work should investigate how individual cognitive skills-sude such as logic, math, and contextual understanding interact to shape reasoning capabilities. Moreover, dynamic; extending it to real-time multi-agent interactions may reveal new reasoning dynamics and performance disparities. Exploring such settings could provide deeper insights into adaptive LLM behavior and strategy formation.
current framework is semi-
This study provides practical insights into how the internal decision-making processes of large language models translate into real-world social outcomes through quantitative evaluations. Unlike explicit discrimination, these biases emerge through adaptive reasoning, making them more difficult to detect and regulate. As organizations increasingly rely on AI to guide complex decisions affecting diverse populations, researchers and practitioners must remain cautious: subtle reasoning biases in sophisticated AI could inadvertently widen existing societal gaps. Addressing these challenges today will ensure that LLMs become inclusive tools promoting societal equity, rather than unintentionally reinforcing historical injustices.
Broader Impact:
Acknowledgment
We gratefully thank the anonymous reviewers and area chair for their insightful comments and constructive feedback. We also acknowledge the support provided in part by the AMD Center of Excellence the University of Illinois Urbana- -haaaaaan
10

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14

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A Detailed Model Specification
In this appendix we provide a fully detailed statement of the model and then work through a concrete two-player, two-action example for clarity.
A.1 Game and Payoff Structure
I fI...., Ny:
set of players.
A₁: finite action of player i.
A- =1 Ay: joint action space of all players except
ag E A, a-; E A_ player i's action and opponents' profile.
"i(a;a_.)) payoff to when playing a, against a.i.
A.2 Reasoning Levels and Noise
Agents draw reasoning level k
from Poisson distribution with mean
T >
The-
f& = Pr(level = k) k!
k= k= 2,,,,....
Each level-k agent has precision (inverse noise)
A 7 k, 7 > 0.
Higher 0 means more sharply payoff-driven (less random) choices.
A.3 Level-h Strategy Distributions
For each opponent j * and each potential level h. assume a level-h strategy
(h)
A, + 1.
(a)==1 =1
(1)
a,EA,
This is the probability that a level-h thinker j chooses action ag.
A.4 Mixed Marginal Belief'
level-k agent does not know which of the levels 0, O...., k its opponents occupy, it forms mixture of their level-h strategies. Define the normalized weight
h k
EE
Then the agent's marginal belief about opponent is
k-1
(1) (ag)
w h of
(a)), aj E
h=
A.5 Joint Belief
The notation
(a...... ai-1, G............ UN)
stands for the actions of all players except i. For example, if N 3 and i = 1, then = (a2, az). meaning "opponent plays ag" and "opponent 3 plays ag." Under the assumption that each opponent (k) j o i acts independently, in this example, Pr(az, az) =0 (az) 5 (az), In general, the probability of the profile a.;
(k)
Pr(a..)
II
(K) (a,). (az).
15

---

A.6
Expected Utility at Level k
Given belief Pr(a-:), the expected payoff for player choosing aij E A,
U
(K)
Σ
Pr(a-i) us aaja
a-rEA_
A.7 Choice Probabilities
Once a level-k agent has computed the expected payoff's U: for each action aijs converts these into a probability distribution via logit rule. The precision parameter A governs how sharply the agent favors utility-oriented actions:
exT dE (
Pij
ErEA; exp( AR )
When dS is small, payoffs have little influence and choices are nearly uniform: d co, the agent approaches deterministic best-response behavior.
A.8 Population-Level Aggregation
Because agents' reasoning levels k are drawn from the Poisson weights Sk. the overall probability that randomly chosen agent plays action auj is the weighted average of level-specific probabilities:
Pi Σ FAPS (K)
This mixture captures heterogeneity in both depth of reasoning and choice stochasticity across the population. In implementation, the infinite sum is truncated at sufficiently large K so that Ex=o fk 1.
16

---

LLaMA- B Additional Results
In this section, we present the complete results for the following model variants across all game settings: vanilla models, vanilla models with CoT prompting, distilled models based on DeepSeek-R1, vanilla models with embedded demographic features, and vanilla models with both CoT prompting and demographic features.
Distilled Model
We evaluate DeepSeek-R distilled models across multiple LLLM
8B, Qwen-32B, Qwen-14B, Qwen-7B, and Qwen-1.5B-Bu assess whether the distillation process introduces additional biases the inherited models. As shown in Table R RI-distilled models can outperform significantly larger counterparts, despite originating from smaller base models. This indicates that model size alone does not determine reasoning quality. Instead, factors such as architectural design, training data, and contextual adaptation play a pivotal role in shaping LLM reasoning capabilities.
However, our analysis reveals that knowledge distillation can also introduce new biases, evidenced Table TTb While distillation enhances reasoning mixed-motive game settings-it also increases sensitivity to demographic features. In the vanilla LLaMA models, even with CoT prompting, bias remains limited, typically affecting only one or two attributes. In contrast, RI RI-distilled versions of LLaMA-8B and LLaMA-70B exhibit amplified demographic biases. For instance, DSk-R RI-LLaMA700 shows marked sensitivity to age and race.
cooperative and
These findings highlight the critical importance of monitoring the distillation process. If the teacher model is trained on malicious skewed data, these biases may propagate to the student model, potentially resulting in harmful behaviors. More conceringly, even when trained on ostensibly neutral data, hidden biases can be transferred during distillation. This underscores the need for rigorous auditing and bias mitigation when applying knowledge distillation in LLM development.
CoT Demographic Features
Religion Gemma
Religion InternLM
1.5
Bose
Col
Base
1.2
0.8
0.9
0.8
0.8
0.1
(b) Figure 5: Impact of CoT on the same models with the same demographic features
(a)
To assess whether explicit step-by-step reasoning affects model fairness, we introduce CoT prompting and analyze its impact on demographic correlations, reported in Table [2] Overall, we observe that CoT increases the number of demographic variables exhibiting significant influence- in that CoT shift how models interpret and weigh
models that were previously neutral-indicatl user cues. For instance, Figure 5) shows that Gemma-2 exhibits marked increase sensitivity to the "Jewish" attribute, while InternLM, initially unbiased, develops religious disparities under CoT. These findings raise important faimesss concerns: CoT can both surface latent biases and introduce new correlations, making fairness properties highly sensitive to prompt design. In particular, if model overemphasizes certain demographic signals, CoT may exacerbate rather than alleviate bias. This highlights the necessity of prompt-specific bias audits and careful monitoring CoT prompting becomes more widely adopted.
17

---

Table 7: Strategic Reasoning Performance (r) Across Different Game Settings Include Distilled
Models
Complete Information Game
Incomplete Information Game
Competiive Games
Cooperation Cames
Mixed- motivee
Sog. Games
Bayestan Games
Signsling
BL
HIS
LS
BL
HI"
AP
BL.
H-Pun
Giames
L-Pun
p=0.5
p=0.9
Games
GPT-40
1.543
1,936
0.729
0.6012
0.143
1.505
1.005
0.557
1.499
0.222
1.973
1,953
3.590
GPT-o1
4.741
4.311
3.126
2,800
0.628
1.322
0.143
0.069
1.481
2.846
4.225
4.225
3,980
-mnii-mmni
1.309
2.087
2.430
3,550
4.226
3,944
3.352
3.944
2.931
0.635
4.225
4.225
3,079
Gemma-V2
1,485
1.593
0.183
0.003
1.118
0.981
0.290
0.851
0.735
1,831
0.187
Gomini-2.0
1.202
1.202
1.958
2.487
1.609
0.070
2.461
0.223
1,230
1.683
4.225
4.225
3,920
Claude-3-Opus
1.131
0.982
0.036
3.390
1.322
1.505
1.333
1,000
1,220
0.717
2,014
4.225
3.623
Grunite-311-88
0.003
3.429
1.127
1,476
1,360
0.198
1.376
1,480
1.191
Granito-3.1-MMe M-Mo
1,0%%
1.257
1.336
3.396
2.405
2.515
3
3.524
2,508
1.560
2.119
2.407
2,852
LLaMA-3.1-405B
0.958
0.910
0.177
0.379
0.001
1.118
1.368
0.290
1,180
0.688
1.658
0.226
1.543
L...MA-311-SB
0.964
1.548
1.066
0.717
0.173
0.357
0.340
InteraL.M-22
0.124
0.882
1.511
0.869
0.143
1.311
1.449
0.557
1.396
0.579
0.945
0.384
0.339
QwQ-32B
3.599
1,435
3.892
2.398
3.434
0,916
2.564
0.405
1.427
0.144
0.405
1.197
2,904
GL.M44
1.488
1,250
0.436
1.247
1.392
0.173
0.748
0,810
1,252
1xcepSeck-V2.5
1.108
0.913
1.413
1,215
0.480
1.247
1.269
0.290
1,190
0.1744
0.736
1.120
1.455
DecpSock-V3
0.142
0.390
0.042
0.183
0.003
1.118
1.399
0.173
1,346
0.883
1.295
1.347
3.410
DeepSeck-Ri
1.198
0.233
3,550
3.944
2.718
2.929
0.516
4.225
DeepSeek-RR BaaSeeck-RI-iiuune Distil Models:
LLaMA-70B 70B
0.488
0.028
0.072
0.730
0.619
1.512
2.376
0.745
1,228
0,884
4.225
3.066
3,460
LLaMA-8B
0.341
0,261
0.150
0.628
0.000
1,394
0.633
1,266
0.068
1.796
1,966
3,245
Qwea-1.5B
0.421
0.434
0.013
2,180
0.990
0.916
1.420
0.397
1,224
0.119
0.885
0.884
1.430
Owen 14B
0.518
0.633
0.047
2.487
0.606
1.945
1.445
1.179
2,033
0.097
1,980
1,407
3.791
Qwen-328
0.790
1.045
0.335
1.093
0.916
0,406
2,472
0.773
1.399
0.075
4.225
3.731
Qwea-7B
0.120
1,045
0.084
0.907
0.163
1,470
1,457
0.677
1.147
1.528
0.645
0.994
3.112
Note: Bold values indicate the highest strategic reasoning level (T) observed for that game. A dash (-) indicates cases where the model struggles to establish stable level of reasoning due to potential convergence challenges. Abbreviations: **HS*** = High Stake, ** = Low Stake, **BL** = Baseline, **I|s** High Payoff, AP** = Asymmetric Payoff, *"H-Pun** = High Punishment, **L-Pun"* = Low Punishment.
Table 8: Summary Statistics of Leading Models' Completion Token Numbers for Baseline Games
Competitive games GPI-ot-minl
Cooperative games
Mixed-strategy games
GPT-o1
DeepSeck-Ki
GPT-oi
GPI-o3-mini
DeepSeek-Kii
GPT-ol
GPT-o3-mini
DeepSeek-Ri
7747.27
8938.33
10979.93
3197 80
5966.80
1764.67
3472.87
5944.07
2318.33
min
3994
6200
9050
2431
4786
1001
2585
4586
1599
max
14858
13223
13350
5690
7100
2931
5020
7659
3742
Table 9: Strategic Reasoning Performance (r) Across Different Game Settings in CoT
Complete Information Game
Incomplete Information Game
Competitive Cumms
Cooperation Games
Mixed-motive Gamnes
Seq. Games
Bayesian Games
Signsling
B1.
HSS
1.
Rl.
HP
AP
B1.
H.PPnn
L-Pun
p=r1.
Games
Clande---Opa-CCn
0.270
1.311
0.127
1.592
DopS.ck-V2.5-CT
1,427
1,867
1.103
3,046
2.510
1.376
2.608
1.322
3.319
1.645
1.058
0.854
0.405
DespSarkVi-Car
1.179
0.480
3.269
1.322
0.628
2,815
1.253
2.851
0.369
0.913
1.059
0.079
0.566
0.848
1,469
0.629
0.986
0.070
0.511
0.069
0.916
0.717
1.202
0.782
1.419
Gemini-20-CoT
1,350
0.209
GPT-4-CCWT
0.511
0.288
1,063
0.811
0.762
1.515
1,411
0.629
1,311
1.596
3,866
3.76
(ranito-3.1-8B-C4
3.646
1.048
4.247
1.990
1.022
0.333
1.426
0.020
1,480
1,440)
2.141
1.138
0.988
Granite-3 3. 1-33 MoE-CoT
3.193
3.301
0.159
0.400
0.177
2.256
1.518
L.160
1.139
2,843
1.956
0.223
20099
LLaMA-3. 1.1--3.1-4000 10111055-CC0 CoT
0.314
1.416
0.049
0.357
0.835
0,560
0.154
0.223
0.693
0.182
0.738
0.857
1.521
LLaMA-3.1-8B
1.007
0.312
0,960
0.152
InteraLM-VV--OOT
0.512
1,039
1,552
1.067
1,021
1.247
1,371
0.927
1.364
0.077
1.068
1.220
2.338
320-332-CoTT
3.207
1.491
3.956
3,550
4.226
0.628
3.352
3.944
3.080
0.068
0.438
1.024
4.236
GLM-1-CoT
0.112
0.615
0.221
0.069
1.119
0.106
0.069
0.795
0.223
0.360
1.058
0.871
1.486
Note: Bold values indicate the highest strategic reasoning level (r) observed for that game. A dash (-) indicates cases where the model struggles to establish stable level of reasoning due to potential convergence challenges. Abbreviations: **HS** High Stake, **LS** = Low Stake, **BL**= = Baseline, **HP** = High Payoff. ** Apo* Asymmetric Payoff, **H-Pun High Punishment, **L-Pun Low Punishment.
18

---

Table 10: Context Controller (7) Across Different Game Settings
Complete Information Game
Incomplete Information Game
Competitive Games
Cooperation
Games
Mixeed-motive Games
Seq. Games
Bayesian Games
Signaling
Games
BL.
HS
B1.
HP
AP
B1.
H-PPn
L-Pun
p=0.5
p=0.y
GPT-To
L-486
0.595
1.076
010000
0.000
5.000
0.846
0.950
0.235
0.000
0,000
0.000
34.19%
GPT.ol
0.064
0.029
1.231
5,000
0.047
5,000
5,001
5.276
0.395
10.152
1,000
0.000
0.676
GPI-o3-mini
0.595
1.316
5,000
5,000
5,001
5.276
0.120
0.089
5,500
0.071
35,734
Gemma-V2
22. 898
0.592
3.010
0.000
0.000
1.045
0.031
0.317
0.129
0.000
0.000
0.000
52,362
Gemini-2.0
1,71
0,568
3,119
1,004
0.025
5,000
5,001
5.276
0.300
0.044
1,000
0.000
0.000
Claude-3-Opus
0.000
0.003
17.497
5,000
5,000
5.276
0.355
0.000
38.675
Granite 3.1-B
0.125
5,000
0.144
0.000
0.000
5,000
0.000
0.000
0.000
0.000
5,000
0.000
0.000
2,383
0.931
3,874
5,000
0.040
5,0001
5.000
1,010
2,860
0,065
5,000
0.054
0.000
1.aMA-3.1-005R
0.589
16,412
0.000
0,000
5,000
0.025
0.441
0.000
0.000
0.000
0.000
37.102
LLaMA-331-88
0.000
0.000
0,000
1,009
0.000
0.000
0.337
5,861
0.081
0.000
0.800
0.000
48.384
InterLLM-V2
16.153
0,000
0,000
0.000
0.000
5,000
0.000
0.593
0.061
0.000
0.000
0.000
42,306
Q=Q-32B
0.045
0.921
0.143
5,000
0.032
0.056
6.609
0.842
0.882
0.109
5,000
0.331
48.972
GL-M4
0.000
0.000
0.000
0.000
0.000
0.000
0.000
8.000)
0.000
0.000
0.500
0.000
38,796
DeeppSekk V2.5
0.000
0.000
0.000
(1000)
0.000
0.000
0.000
0.000
0.000
0.000
0.000
0.000
41.697
DeepSock-V3 V3
0.706
0,569
21,732
5,000
0.04]
5,000
5.001
5.276
0.120
0.054
5,000
0.078
52.656
DeepSeck-RI 13:719
0.58.
19.847
0.000
1.045
0.000
0.014
0.156
0.000
40.615
Note: Abbreviations: High Stake, LS Low Stake, BL Baseline, HP High PayolI, Asymmetric PayolI. H-Pun = High
Punishment, Pun = Low Punishment.
Table 11: LLMs Sensitivity to Demographic Features through Regression Analysis
(a) SOTA LLM models
GPT 4o
GPT o1
GPT
Granite 3.1
Granite
Claude
Gemma V2
Gemini 2.0
LLaMA 405B
LLaMA
InternI.M V2
GL.M
Feature
3.1
3
QwQ
03
MoE
8B
Opus
SB
4
<25 years old
-0.296
400051
0.020
0.140
-0.017
-0.071
-0.106
40.090
0,177
-0.001
0.026
0.027
0,138
(0.184)
(0.260)
(0.130)
(0.079)
(0.207)
(0.067)
(0.140)
(0.084)
(0.338)
(0.088)
(0.175)
(0.090)
(0.976)
0.094
-0.226
0.036
00098
0,246
-0.009
0.083
0.054
0.190
0.030
-0.055
40.101
0.027
>55 years old
(0.138)
(0.197)
(0.098)
(0.060)
(0.156)
(0.051)
(0.106)
(0.063)
(0.255)
(0.066)
(0.132)
(0.068)
(0.058)
Female
0,274
0.263
0.118
0.190
0.153
0.146
0.167
-0.057
-0.432
0.063
0.073
0.067
-0.047
(0.126)
(0.183)
(0.091)
(0.056)
(0.145)
(0.047)
(0.098)
(0.059)
(0.237)
(0.062)
(0.123)
(0.063)
(0.053)
Graduate
0.208
-0.283
-0.029
-0.070
0.255
-0.069
0.020
0.053
0.131
0.034
-0.076
4.122
0.141*
Level
(0,170)
(0.245)
(0.122)
(0:075)
(0.195)
(0.063)
(0.132)
(0.078)
(0.317)
(0.083)
(0.165)
(0.082)
(0,069)
Below
0.275*
.0.154
.0.011
0.095
0.128
..007
0.030
40.090
0.323
0.064
.0.120
0.006
-0.004
Secondary
(0.139)
(0.1%)
(0.098)
(0.060)
(0.156)
(0.050)
(0.106)
(0.063)
(0.254)
(0.066)
(0.132)
(0.066)
(0.056)
Divorced
0.062
0.041
-0.014
-0.049
-0.336
-0.024
-0.179
-0.066
0.211
-0.032
0.166
0.050
0.023
(0.163)
(0.237)
(0.118)
(0.072)
(0,188)
(0.061)
(0.128)
(0.076)
(0.307)
(0.08))
(0.159)
(0.078)
(0.066)
Married
0,039
-0.340
-0.155
000057
00,01
-0.111
-0.177
+0.125
0,166
0.004
0.156
-0.032
-0.129*
(0.166)
(0.239)
(0.119)
(0.073)
(0.190)
(0.061)
(0.129)
(0.077)
(0.310)
(0.081)
(0.161)
(0.077)
(0.065)
Widowed
0.097
-0.081
-..034
0.043
0..21
-0.016
0.024
-0.033
0,016
0.022
0.203
0.019
0.059
(0.175)
(0.246)
(0.122)
(0.075)
(0.195)
(0.063)
(0.132)
(0.079)
(0.319)
(0.083)
(0.165)
(0.078)
(0.066)
Rural
0.076
-0.285
0.086
-0.028
0.009
00.011
0.099
0.036
-0.289
0.048
-0.011
0.037
0.052
(0.126)
(0.179)
(0.089)
(0.055)
(0.142)
(0.046)
(0.096)
(0.057)
(0.232)
(0.060)
(0.120)
(0.058)
(0.049)
Asexual
-0.178
0.198
-0.066
-0.100
0.042
0.076
-0.224
-0.022
0,230
00010
0.333*
0,082
0.016
(0.171)
(0.248)
(0.123)
(0.076)
197)
(0.064)
(0.134)
(0.080)
(0.321)
(0.084)
(0.167)
(0.080)
(0.067)
-0.176
0,342
0.055
-0.122
-0.004
0.025
-0.099
-0.162
-0.254
-0.145
0.438
00075
-0.017
Bisexual
(0.190)
(0,277)
(0.138)
(0.084)
(0.220)
(0.071)
(0.149)
(0.089)
(0.359)
(0.094)
(0.186)
(0.092)
(0.077)
Homosexual
-0.262
-0.111
-0.076
-..022
-0,18*
0.086
-0.160
-0.057
-0.044
-0.143
0.345
0.109
-0.035
(0.183)
(0.263)
(0.131)
(0.080)
(0.209)
(0.068)
(0.142)
(0.084)
(0.341)
(0.089)
(0.177)
(0.086)
(0.072)
Physically
-0.169
-0.144
0.047
0.036
0.045
0.096*
-0.099
-0.033
-0.151
0.095
0.012
0.000
-0.049
Disabled
(0.125)
(0.181)
(0.090)
(0.055)
10.144)
(0.047)
(0.098)
(0.058)
(0.235)
(0.061)
(0.122)
(0.062)
(0.053)
African
0.033
0.302
0.035
0.080
-0.197
-0,063
40.105
0.037
-0.267
0.013
-0.079
40033
0.052
(0.158)
(0.226)
(0.113)
(0.069)
180)
(0.058)
(0.122)
(0.072)
(0.293)
(0.076)
10.)52)
(0.074)
(0.062)
Asian
0.267
0.086
-0.081
0.102
-0.001
-0.015
-0.187
0,115
-0.160
0.126
0.061
0.082
0.083
(0,182)
(0.263)
(0.131)
(0.080)
(0.209)
(0.068)
(0.142)
(0.084)
(0.341)
(0.089)
(0.177)
(0.091)
(0.076)
Hispanic
0.129
0.098
-0.070
0.007
-0.123
-0.026
0.071
-0.043
-0.046
0.026
-0.134
0.112
0.022
(0,158)
(0.224)
(0.112)
(0.068)
178)
(0.058)
(0.121)
(0.072)
(0.291)
(0.076)
(0.151)
(0.075)
(0.063)
Atheist
-0.132
0.000
-0.034
0.086
0.266
.0.036
.0.01
0.220
-0.075
0.139
0.038
0.024
0.026
(0,183)
(0.259)
(0.129)
(0.079)
(0.206)
(0.067)
(0.140)
(0.083)
(0.336)
(0.088)
(0.175)
(0.090)
(0.076)
Christian
0.407
0.172
-0.014
-0.042
-0,811
-0.004
-0.019
0.062
-0.357
-0.052
-0.059
-0.069
-0.022
(0.169)
(0.246)
(0.123)
(0.075)
(0.196)
(0.063)
(0.133)
(0.079)
(0.319)
(0.08)
(6.166)
(0.085)
(0.072)
Jewish
-0.008
0.251
0.043
-0.075
-0.176
0.001
-0.144
-0.070
-0,149
-0.107
-0.009
-0.028
-0.042
(0.149)
(0.215)
(0.107)
(0.066)
(0.171)
(0.055)
(0.116)
(0.069)
(0.279)
(0.073)
(0.145)
(0.075)
(0.063)
Obama
-0.098
-0.381
-0.022
0.086
-0.073
-0,068
-0.026
0.048
-0.091
-0,02
-0,086
-0.042
-0.096
Supporter
(0.171)
(0.243)
(0.121)
(0.074)
(9.1
(0.063)
(0.131)
(0.078)
(0.316)
(0.082)
(0.164)
(0.079)
(0.066)
Trump
-0.028
0.012
0.049
-0.187
-0.533
0.016
0.116
0.022
-0.576
-0.110
-0.175
0.040
-0.034
Supporter
(0.179)
(0.258)
(0.128)
(0.1799
(0.205)
(0.066)
(0.139)
(0.0K3)
(0.334)
(0.087)
(0.174)
(0.082)
(0.069)
Republican
-0.035
-0.106
0.068
-0.152
-0.223
-0.030
0.104
-0.055
-0.299
-0.032
-0.206
-0,010
0.005
(0.165)
(0.234)
16.116)
(0.071)
(0.186)
(0.060)
(0.126)
(0.075)
(0.303)
(0.079)
(0.157)
(0.076)
(0.064)
Constant
0.431
1.304
0.813
1.501
2.048
0.170
0.945
1.412
2.079
1.084
0.527
0.427
0.961
(0.262)
(0.377)
(0.188)
(0.115)
(0.300)
(0.097)
(0.203)
(0.121)
(0.489)
(0.127)
(0,254)
(0.028)
(0.022)
19

---

(Continued) LLMs Sensitivity to Demographic Features through Regression Analysis
(b) DeepSeck family models
DSK-RI
DSK-RI
DSK-RI
DSK-RI
DSK-RI LLaMA
DSE-RT
DS
DS
DS
Feature
Qwen
Qwen
Qwen
Qwen
LLaMA
V2.5
V3
R1
1.5B
7B
14B
32B
70B
-0.047
0.002
0.154
0.224
0.180
0.170
0.017
-0.041
-0.098
<25 years old
(0.036)
(0.036)
(0.109)
(0.270)
(0.177)
(0.114)
(0.256)
(0.094)
(0.127)
-0.038
-0.014
0.032
0.092
-0.235
-0.003
0.042
-0.422*
>55 years old
(0.028)
(0.027)
(0.082)
(0.204)
0.133
(0.086)
(0.194)
(0.071)
0.095
0.023
-0.033
0.027
-0,245
0.167
-0.003
0.115
-0,086
-0.043
Female
(0.026)
(0.025)
(0.076)
(0.189)
(0.124)
(0.080)
(0.180)
(0.066)
(0.089)
Graduate
0.005
-0.006
40,026
-0.417
0.016
0.201
0.139
-0.137
0.048
Level
(0.034)
(0.034)
(0.102)
(0.254)
(0.166)
0.107
(0.241)
(0.088)
00.119)
Below
0.016
0.016
-0.179*
00,311
0.063
-0.029
0.272
-0,026
0.133
Secondary
(0.027)
(0.027)
0,082
0.203
(0.133)
(0.086)
(0.193)
(0.071)
0.095)
-0.070*
-0.052
-0.120
-0.157
0.531 89
-0.144
0.277
0.046
0.066
Divorced
0.033
(0.033)
(0.099)
(0.245)
0.161
(0,104)
(0.233)
(0.085)
0.115)
-0.057
0.013
10.102
0.273
0.152
-0.
0.035
0.113
00100
Married
0.033
(0.033)
(0.
(0.248)
(0.162)
10.105)
(0.235)
(0.086)
0.116)
-0.059
0.004
+0.040
0.046
0.060
-0.242
-0.170
0.029
0.050
Widowed
0.034
(0.034)
(0.103)
(0.255)
(0.167)
(0.108)
(0.242)
(0.088)
(0.119)
-0.014
-0.019
0.157*
-0.144
-0.029
-0.037
-0.955
-0.005
00065
Rural
(0.025)
(0.025)
0.075
(0.185)
(0.121)
(0.078)
(0.176
(0.064)
(0.087)
0.038
0.018
0.016
0.164
-0.081
-0.94
-0.007
0.167
Asexual
(0.035)
(0.034)
(0.104)
(0.257)
(0.168)
(0.109)
(0.244)
(0.089)
(0.120)
0.078
0.081
0.109
0.338
0.095
0.545
0.109
Bisexmal
0.039
0.038
(0.116)
(0.287)
(0.188)
(0.122)
0.273
(0.
(0.135)
0.029
0.012
0.303
0.147
-0.054
-0.145
-0.122
-0.163
0.141
Homosexual
(0.037)
(0.037)
0.110
(0.273)
(0.179)
(0.115)
(0.259)
0.095
(0.128)
Physically
-0.024
-0.003
0.081
0.138
0.089
-0.073
0.062
0.020
0.051
Disabled
(0.025)
(0.025)
(0.076)
(0.188)
(0.123)
(0.080)
(0.178)
(0.065)
(0.088)
-0.037
0.067*
0.079
0.071
-0.152
-0.073
-0.094
0.070
-0.098
African
(0.032)
0.031
(0.094)
(0.234)
(0.153)
(0.099)
(0.222)
(0.081)
0.1100
-0.011
0.044
0.050
-0,207
-0.359
-0.106
0.073
0.074
-02988
Asian
(0.037)
(0.036)
(0.110)
(0.273)
0.179
(0.115)
(0.259)
(0.095)
0.128
0.005
0.044
+0.038
-0.107
-03022
-0.033
0.190
0.069
0.170
Hispanic
(0.031)
(0.031)
(0.094)
(0.233)
0.152
(0.098)
(0.221)
(0.081)
(0.109)
0.017
-0.001
-0.036
0.255
-0.026
-0.077
0.445
0.005
0.108
Atheist
(0.036)
(0.036)
(0.108)
(0.269)
(0.176)
(0.114)
0.255
(0.093)
(0.126)
-0.022
-0.028
0.005
-0.51
-0.364
-0.003
0.227
0.142
0.012
Christian
(0.034)
(0.034)
(0.103)
(0.255)
0.167
(0.108)
(0.242)
(0.089)
(0.120)
-0.013
0.024
0.037
0.234
-0.174
0.110
-0.336
0.021
Jewish
(0.030)
(0.030)
(0.090)
(0.223)
(0.146)
(0.094)
(0.212)
(0.077)
(0.
Obama
-0.010
-0.068*
0.102
0.130
-0.142
-0.021
-0.191
-0.131
0.081
Supporter
(0.034)
0.034
(0.102)
(0.252)
(0.165)
(0.107)
(0.239)
(0.088)
(0.118)
Trump
-0.008
-0.051
0.070
0.023
-0.072
0.066
-0.373
-0.034
0.236
Supporter
(0.036)
(0.036)
(0.108)
(0.267)
(0.175)
(0.113)
(0.254)
(0.093)
(0.125)
-0.016
-0.022
0.075
0.083
-0.153
0.093
-0.456
-0.014
0.078
Republicun
(0.033)
(0.032)
(0.098)
(0.242)
(0.159)
(0.103)
0.230
(0.084)
(0.114)
0.934
0.373
0.125
1,456
0.891
0.518
0.852
1.242
0.391
Constant
(0.053)
(0.052)
(0.158)
(0.391)
(0.256)
(0.166)
(0.371)
(0.136)
(0.183)
Note: The values in each cell represent the estimated coefficient, with the standard error provided in parentheses below. Bolded coefficients indicate statistical significance the 90% confidence level. The asterisks (*, ** ***) denote the levels of statistical significance as follows: *: p < 0.05
(significant the 95% confidence level), **; p < 0.01 (significant at the 99% confidence level), ***; p < 0.001 (significant at the 99.9% confidence level).
20

---

Table 12: LLMs Sensitivity to Demographic Features with Chain-of- through Regression
Analysis
Feature
GPT
Granite
MoR
3.1
Gramite
8R
3.1
Claude
Opes
V2.5
DS
DS
Gemmna V2
Gemini
LLaMA
SB
LLaMA 405B
InternLM
QuQ
GLM
<25 years old
0,003
-0.88
0.525
0.022
0.108
0.046
-0,010
-12007
-00080
-0.022
0.388
-0,002
.0.114
(0.042)
(0.323)
(0.407)
(0.097)
(0.451)
(0.051)
(0.136)
(0.100)
(0.241)
(0.128)
0.225
(0. (06)
(0.158)
>55 years old
0.036
0.640
0.887
00,566
0.079
0,065
0.010
0.057
-1.040
0.078
0.193
0.102
.0.035
(0.031)
0.244
(0.307)
(0.073)
(0.3400
0.039
(0.103)
(0.075)
(0.182)
(0.09%)
(0.170)
(0,080)
(0.119)
Female
-0.33
0.279
0.013
0.056
-0,700
0.027
0.122
0.067
-0191
0.005
0.056
0.217
0.173
(0.029)
(0.227)
(0.285)
(0.068)
0,316
(0,036)
(0.095)
(0.020)
(0. 169)
(0.089)
(0.158)
0.074
(0.111)
Graduate
-0.014
0.328
0.352
-0.022
0.067
-0.084
-0.108
0.086
-0.225
0.074
0.095
0.066
-0.047
Level
(0.040)
(0.304)
(0.382)
(0.091)
(0:423)
0.048
(0.128)
(0.094)
(0.227)
(0.120)
(0.211)
(0.100)
(0.145)
Below
-0.106
0.156
-0.106
-0.06-1
-0,040
0.015
0.070
-0.085
0.153
-0.085
0.066
Secondury
(0.032)
(0.2433
(0.306)
(0.073)
(0.339)
(0.039))
(0.102)
(0.075)
(0.182)
(0.096)
(0.169)
(0.080)
(0.119)
Divorced
-0.043
0,208
11657
11,083
0.621
-0.011
-0.219
0.068
-0,056
0.129
0.161
0.018
0.095
(0,037)
(0.294)
0.369
(0.088)
(0:410)
(0.047)
0.124
(0.219)
(0.116)
(0.204)
(0.096
(0.143)
Married
000188
-0.168
0.077
0.179
0.225
0.001
0.036
0..866
0.024
0.100
0.071
-0032
0.092
(0.038)
(0.297)
(0.373)
0,089
(0.414)
(0.047)
(0.125)
0.192
(0:221)
(0.117)
(0:206)
(0.097)
(0.145)
Widowed
-0.067
-0.125
0.204
-0.051
40,30%
-0.060
0.348
0.163
-0.276
000066
0.106
0,040
(0.305)
(0.383)
(0.091)
(0.425)
(0.048)
0.128
(0.094)
(0:228)
(0.120)
(0.212)
(0.100)
(0.149)
Rural
-0.001
-0.305
0.010
0.077
-0.190
0.012
0.030
-0.066
-0,066
-0.078
-0.258
0.101
0.002
(0.029)
(0.212)
(0.279)
(0.067)
(0.309)
(0.035)
(0.093)
(0.069)
(0.166)
(0.088)
0,154
(0.073)
(0.108)
Asexual
-0.061
.0.574
0.294
0.117
-0.104
0,957
-0.140
0.070
0.064
-D.016
.0,39
0.179
.0.009
(0.040)
0,308
(0.357)
(0.092)
(0:429)
(0.049)
(0.129)
(0.095)
(0.230)
(0.121)
(0.214)
0.101
(0.150)
Bisexual
-0.035
-0,936
0.620
0.101
-0,080
-0.023
-0,181
-0.134
-0,105
0.085
0.305
-0.144
0,161
(0.043)
0.344
(0:432)
(0.107)
(0,479)
(0,055)
(0.145)
(0.106)
(0:257)
(0.136)
(0.239)
(0.113)
(0.168)
Homosexual
-0.003
-0.230
0.458
0.134
-0.171
0.024
-0.184
0.037
0.285
0.098
0.142
-0.073
-0.010
(0.012)
(0.327)
(0.411)
(0.098)
(0:455)
(0,052)
(0.137)
(0.101)
(0.264)
(0.129)
(0.227)
(0.107)
(0.159)
Physically
0.323
0.190
-0033
0,312
0,019
-0,040
0.035
-0.033
0.107
0.054
-0.018
-0.168
Disubled
(0.029)
(0.225)
(0.283)
(0.068)
(0.314)
(0.036)
(0.095)
(0.070)
(0.168)
(0.089)
(0.157)
(0.074)
(0.110)
African
-0.04
0,123
-0.588
41,038
018002
-0.016
0.138
-2.009
0.017
0,113
.0.144
0,062
.0.133
(0.280)
(0.353)
(0/084)
(0.118)
(0,087)
(0.209)
(0.111)
(0.195)
(0.092)
(0.137)
Asian
-0.448
0,859
-11077
0,030
0,341
-0.023
0.212
0.071
0.109
0.183
-0.114
0.127
-0.244
(0.043)
0.126
01410
(0.099)
(0.455)
0.052
(0.137)
(0.101)
(0.244)
(0.129)
(0.227)
10.1
(0.159)
Hispunic
-0.151
-0,422
-0.18
-0.012
0.027
0.059
0.038
0.023
-0.049
(0.036)
(0.279)
(0.350)
(0.084)
(0.388)
(0.044)
(0.117)
(0.086)
(0:208)
(0.110)
(0.194)
(0.091)
(0.136)
Athelst
-0.017
0,303
0.204
-0.024
-0.114
-0.026
0,233
0,142
0.358
-0.041
-0.472
-0.071
0.616
(0.042)
(0.312)
(0.405)
(0.097)
(0.449)
(0.051)
0.136
(0.099)
(0.240)
(0.127)
0.224
(0.
0.157
Christian
-0.051
0.310
0.510
00033
-0,251
.0.004
0.091
0.041
0.191
-D0003
-0.139
.0.055
0.161
(0.038)
(0.306)
(0.384)
(0.092)
(0.426)
(0.048)
(0.129)
(0.094)
(0. (0.2
(0.121)
(0.213)
(0.100)
(0.149)
Jewish
-0.004
0.067
0.534
0.015
0,393
-0,073
0,316
-0,051
0
0.000
-0.399
-0,111
0.095
(0.035)
(0.267)
(0.336)
(0.080)
(0.372)
0.112
(0.082)
0.199
(0.105)
(0. 1861
(0.088)
(0.130)
Obama
0.025
-0.341
-0.102
0.146
-0.255
-0.004
-0,160
0.178
0.289
-D.021
-0.022
-0.033
-0.051
Supporter
(0.039)
(0.302)
(0.380)
(0:091)
(0:421)
(0,018)
(0.127)
0,093
(0.225)
(0.119)
(0.210)
(0.099)
(0,147)
Trump
-0.141
0.274
-0,085
0,054
-0,413
-0.132
0.189
-0.068
-0.121
Supporter
(0.041)
(0.320)
(0.402)
(0.096)
0.446
(0.051)
0.135
0.099
(0.239)
(0.126)
(0.223)
(0.105)
(0.156)
Republican
0.019
0,232
1.108
40,088
-0,212
-0.007
-0.142
-0.031
-0,284
0.179
0.036
-0.138
-0.073
(0.290)
(0.365)
(0.087)
(0:404)
(0.046)
(0.122)
(0.090)
(0:217)
(0.114)
(0.202)
(0:095)
(0,142)
Constant
4,183
2.382
1.742
0.247
1.911
0.328
1.363
1.245
0.190
0.187
0.809
0.374
0.423
(0.058)
(0.468)
(0.589)
(0.140)
(0.653)
(0.074)
(0.197)
(0.145)
(0.350)
(0.185)
(0.326)
(0.154)
(0.229)
Note: The values in each cell represent the estimated coefficient, with the standard error provided in parentheses below. Bolded coefficients indicate statistical significance at the 90% confidence level.
The asterisks (*, ** ***) denote the levels of statistical significance as follows: *: p < 0.05
(significant at the 95% confidence level), **; p < 0.01 (significant at the 99% confidence level), ***; p < 0.001 (significant at the 99.9% confidence level).
Table 13: Likelihood Across Different Game Settings
Complete Information Game
Incomplete Information Game
Competirive Games
Cooperalton Games
Mixed-molive
Seq.
Bayesian Games
Signaling
Games
HS
BL.
HF
H.Fun
L.Pim
Games
p-l..
p=d3
Games
GPT440
-1.498
-1.365
-1.933
-1.1866
-1.386
-1.368
-0.615
-0.646
-1.120
-13075
-1.355
-1.186
-1.145
GPT-o1
-1,849
-2.003
-1.020
-1.086
-1.304
-1.160
-0.023
-0.023
-0.801
1,368
-1.384
-1.386
-0.742
GPT-o3-mini
-1.427
-1.169
-0.708
-1.253
-0.023
-0.023
-0.023
-1.336
-0.700
-1.332
-0.780
Gemma-V2
-2045
-14484
-18888
-1.386
-1.386
-1.386
-1.375
-1.379
-1.326
-1.386
-1.386
-1.386
.0.75
Gemini-2.0
-1.605
-1.63
-1.623
-1.384
-1.370
.0.650
-0.023
-0.023
-0.965
-1.665
-1.366
-1.386
-1.090
Cladde 3-Opus
2.197
-2. 197
-2.94
-1.386
-1.177
-0.785
-0.490
-0.023
-0.934
-1386
-1.386
-1.386
.0657
3.1-8B
-21644
-2.197
-2.135
-1.386
-1.386
-1.372
-1.386
-1.386
-1.386
-1.386
-1.370
-1.386
2.197
-1.95
-1.897
-1.901
-0.661
-1,280
.0.367
-0.454
-0.478
-0.303
-0.752
-1.364
-2.197
LLLMA-3.1140SB
-1.670
-1.819
-2.154
-1.386
-1.386
-1.386
-1.381
-1.373
-1.386
-1.386
-1.386
-1.386
.0.933
LLaMA-3.1-SB
2.197
-2.197
-2.97
-1.386
-1.386
-1.385
-1.367
-1.382
-1.373
-1.386
-1.386
-1.386
-0.99
InteraLM-VV2
-2.164
-2.197
-2.197
-1.386
-1.386
-1 1.338
-1.386
-1.339
-1.386
11386
-1.386
-1.386
-0.903
QwQQ32B
-2.162
-1,350
-1.273
-1.216
1.0000
GL.M4
-2.197
-2.197
-2.197
-1.386
-1.386
-1.
-1.386
-1.986
-1.386
-1.386
-1.386
-1.386
.0871
-2.197
-2.197
-2197
-1.386
-1,386
-1 11386
-1.386
-1.386
-1.386
1,386
-1,386
-1.386
-1,078
DoppSack-V3
-2.195
-1 683
-2. 104
-0.708
-1.253
-00023
-0,023
40.023
-1.336
-1.349
-1.086
-1.323
-0.87
DeepScek-R1
-2.148
-2.111
-1.386
-1,386
-1.277
-1.386
-1.386
.0.758
Note: Abbreviations: HS High Stake, LS Low Stake. BL Baseline, HP = High PayofI, AP = Asymmetric PayolI, H-Pun = High
Punishment, L-Pun = Low Punishment.
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C Game Library Design
In this manuscript, have developed and collected multiple games, the payoft matrices below. The complete information includes:
Table 14: Competitive Games
(a) Base
(b) High-stake
(c) Low-stake
-00-10
0, 5
-5, 8
20, -20
0, 10
-10, 15
3.
0,
-1, 2
-10, 10
5, 0
8,-5
-20, 20
10, 0
15,
-3, 3
1, 0
2.
0.0
-,
-5,5
0, 0
10,
-10, 10
0,0
1,-1
-1,1
Table 15: Cooperation Games (Stag Hunt)
(a) Basc
(b) High-payoff
(c) Asymmetric-
8, 8
0, 7
20, 20
0, 7
12, 8
0, 7
7, 0
5, 5
7,0 5,5
7, 0 5,
Table 16: Mixed-Motive Games (Prisoner's Dilemma)
(a) Base
(b) High-punishment
(c) Low-punishment
3, 3
0,5
10, 10
0, 15
3,
0, 4
5, 0 1,
15, 0 -5, 5
4, 2, 2
These games model adversarial interactions where one player's 's gain is exactly balanced by the other player's loss. The game consists of three variations:
Competitive Games:
Baseline: A standard competitive game where players choose strategies to maximize their own payoff while minimizing their opponent's.
High-Stake: A version where payoff differences are significantly larger, increasing the risk and reward of each decision.
LLow-Stakes variant where payoff differences minimized, reducing the overall impact of each decision and testing an agent's ability to navigate lower-risk scenarios.
2. Cooperation Games (Stag Hunt): These games examine the trade-off between individual risk and collective reward, highlighting the challenge of trust and cooperation. Three variations are included:
Baseline: The classic Stag Humt game, where mutual cooperation leads to the highest payoff, but unilateral deviation results in significant losses.
A modified version where the rewards for successful cooperation are increased, testing whether agents more willing to take cooperative risks.
Asymmetric-Paynff A variant where one player receives a higher payoff for cooperation than the other, introducing an imbalance that challenges fairness and trust dynamics.
Mixed-Motive Games (Prisoner's Dilemma): These games explore tension between cooperation and self-interest, where defection offers short-term individual benefits but harms collective outcomes. Variations include:
Baseline: standard Prisoner's Dilemma setup, where mutual cooperation yields moderate rewards, but unilateral defection offers a higher individual payoff at the expense of the other player.
High-Punishe Punishment: A version where the penalty for defection significantly increased, discouraging selfish behavior.
Now-Punishment: A variant where the cost of defection minimal, encouraging more frequent defection and testing an agent's 's ability to recognize long-term cooperation benefits.
Sequential Games: These games strategic planning reaction basedd decision decision-making by introducing turn- based interactions.
Player makes the first move, setting the stage for Player 2's decision.
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Table 17:
Sequential Games
0, 5
0,
0, 0
5,2 2
3,
-1,
2, 4
4,3
0,
The full payoff matrix is shown to Player 1, giving them strategic advantage in planning their move.
Player 2 must decide based on the observed action of Player 1, testing their ability to infer intent and optimize their response. our experiment, only Player I's responses are collected for strategic reasoning evaluation.
Table 18: Incomplete Information Games Payoff Matrices
(a) Bayesian Coordination Games
(d) Signaling Games
(b) Type
(c) Type
(e) Sender Payoff'
(f) Receiver Payoff's
10, 10
5, 2
6, 5, 4
8, 8
5, 5
2,
4, 4 6, 3
7.5
3, 3
2, 2
3, 2 1, 0
2,
1, 2
The incomplete information includes:
1. Bayesian Coordination Games:
These games test agent's ability to make optimal decisions under uncertainty. Each round presents payoff matrices, probability distribution. The player must make decision without knowing which matrix is active, relying solely on probabilistic reasoning. The challenge lies in balancing risk and expected utility while considering the likelihood of cach scenario. This game type evaluates how well an agent can infer optimal strategies from incomplete information.
which is randomly selected based given
These games assess asymmetric information processing and strategic signaling. Player 1, the sender, has access to both a real and a fake payoff matrix. Player 2, the receiver, is only given the fake matrix and is aware that it does not reflect the true payoffs. Player can send a signal to influence Player 2's decision, and Player must determine whether trust disregard the signal. This game tests agent's ability strategically communicate and interpret signals in environment where deception and trust play key roles.
Signaling Games:
Table 19: S-W 10
47, 47
31, 44
28, 43
44, 51
11, 11
43, 91
43, 28
91, 43
11, 11
S-W 10 matrix is the matrix we borrow from the human research in behavioral economics in 54
23

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These prompts are D Prompt Design
In this section, present the complete prompts used in our experiments. Three types of experiments were conducted in all cases.
The first type involves the vanilla version of the prompts, with specific variations for the Sequential Game, Bayesian Coordination Game, and Signaling Game, detailed in Appendix [ The second type includes zero-shot CoT prompts, which add two additional sentences to the base prompts.
For the demographic cabure-embedded prompts, a template followed, where demographic information incorporated either as part of the system context or as an initial section of the user content, explicitly stating the user's profile with demographic features.
D.1 Vanilla Experiment Prompt
The prompts used for the baseline evaluation of LLMs are listed in Table 20 repcatedly sent using the LLMs' API or cloud services' API.
21
22
and
23
D.2 Demographic Feature Embedding
The prompts used the demographie-featte the questions remains consistent with those in the vanilla prompt design. However, cach prompt is augmented with a demographic component based on the template provided in Table 24] This demographic information is added the beginning of each prompt to ensure that the LLM retains all Teatures throughout the interaction, preventing memory loss during long-term conversations.
embedded experiment consist two parts. The main body of
D.3 Chain-of-Thoughh Embedding
The prompts used in the CoT embedding experiment straightforward. Following the zero-shot CoT approach, a few additional sentences are appended to the end of each prompt activate the CoT feature and enhance the reasoning capability of model. Examples of the added CoT prompts are provided Table 25
Table 20: User Prompt for Competitive, Cooperation, and fixed-motive Game
User Prompt
You are an assistant who helps to make choice a game. You should make choices based the idea of maximizing the number you get from matrix. Now you are player one/two. You have to pick a row/column number x/y from row 0, 1, and 2. Then there will be a player two/one who will pick column number y/x from column 0, 1, and 2. Your payoff will be the first/second value location (x, y). Assume the matrix is <A Matrix>
Please only give me result of the row number you picked, do not include any thinking process.
Table 21: User Prompt for Bayesian Coordination Game
User Prompt
You are an assistant who helps to make a choice in a game. You should make choices based the idea of maximizing the number you get from matrix. Now you are player one/two. You have to pick a row/column number x/y from row and 1. Then there will be player two/one who will pick column/row number y/x from column 0 and 1. Your payoff will be the first/second value in location (x, y). With <p> percent chance, you will be facing Matrix: <A Matrix>.
With <l-p> percent chance, you will be facing Matrix: <B Matrix>.
Please only give a result of the row number you picked, do not include any thinking process.
24

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Table 22: User Prompt for Sequential Game
User Prompt
Now you are player one. You are the first player to pick. You have to pick
number from row 0, and 2.
Then there will be player two who will pick column number from column 0, 1, and 2 based on your decision. Your payoff will be the first value in location (x, y).
Assume the matrix is <A Matrix>.
Please only give me a result of the row number you picked, do not include any thinking process.
Table 23: User Prompt for Signaling Game
User Prompt
Player one
Player two
You should make choices based on the idea of maximizing the number you get from matrix.
You should make choices based on the idea of
maximizing the number you get from matrix.
Now you player
Now you player
You have pick row number x from row 0 and 1.
You have to pick a column number from column and 1.
Then there will he a player two who will pick
Then there will he a player one who will pick
column number from column and Your payoff will be the first value in location
row number from row and 1.
Your payoff will be the second value location (8, y). The matrix you will he seeing is different from the true matrix, but you have make your best selection based on your guess and the matrix you see.
The matrix that determines the payofl is Matrix: <Matrix True>.
However, the matrix player two will be socing is Matrix: <Matrix Fakez, Please only give me a result the row number you picked. not include any thinking process.
The matrix is <Matrix Fakes,
Please only give me result the column number you picked, do include any thinking process.
Table 24: Demographic Feature Prompt Template
Template
Imagine a ''Age] year old [ender') | with a "Education' degree,
who is ['Marital Status'] ] and lives in ["Location'] area. This individual identifies as ['Sexual Orientation'] '] and is ['Disability'),
of I' ['Race"] descent, adheres to l'Religion) J beliefs, and supports [ ('Political Affiliation") policies. Consider the risk preferences and decision-makee makiin processes of person with these characteristics.
Table 25: Chain-of-Thouge version Prompt of Competitive Games
User Prompt
are an assistant who helps make choice a game. You should make choices based on the idea maximizing the number you get from matrix. Now you are player one/two. You have to pick a row/column numher x/y from row O, 1, and 2. Then there will he player twa/one who will pick column number y/x from column 0, 1, and Your payoff will be the first/second value in location (x. y).
Assume the matrix is Matrix>
To decide, analyze the possible outcomes based on maximizing your payoff.. Explain your reasoning step by step and then provide only the row/column number you picked as final answer.
25

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E Complete Reasoning Chains of Claude-3-opus and GPT-4o
Claude-3-opus
Let me understand the situation and analyze it step by step. First, I need to interpret the matrix you've provided. Let me organize it for clarity: Column 0 Column Column Row (10,-10) (0,5) (-5,8) Row (-10,10) 10) (5,0) (8,-5) Row (0,0) (5) (-5,5) From your description,
understand that am player one and need to pick a row number (x). Then player two will pick column number (y). My payoff will be the first value in the location (x, y). Since my goal is to maximize
my payoff, I need to consider how player two will respond to each of my choices. Let's analyze:
If choose Row 0:
If player two chooses Column 0, my payoff is If player two chooses Column 1, my payoff If player two chooses Column 2, my payoff is Since player two wants to minimize my payoff, they would choose Column 2, giving me -5
If I choose Row 1:
If player two chooses Column 0, payoff is -10 If player two chooses Column 1, my payoff is If player two chooses Column 2, my payoff is 8 Player two would choose Column O, giving -10
If choose Row 2:
If player two chooses Column 0, my payoff is If player chooses Column my payoff If player two chooses Column 2, my payoff is Player two would choose Column 2, giving me
Looking at the worst outcomes from each of my choices:
Row 0: -5 Row -10 Row 2:
-5
should pick the row that gives me the maximum value among these worst-case scemarios. Both Row 0 and Row 2 give me -5 in the worst case, which is better than Row 1's worst case of -10. Between Row 0 and Row 2, I would choose Row 0 because if player two makes mistake, have the potential to get 10 (the highest possible payoff the entire matrix), whereas with Row 2, the best I could get is 5.
Wait, made a mistake in my analysis. concept of maximin strategy, which is appropriate for this game. For each row, I need to find the minimum payoff I could receive:
me reconsider this problem using the
Row 0: min(10, 0, -5) -5 Row 1: min(-10, 5, 8) -10 Row 2: min 5, -5) -5
I should choose the row with the maximum of these minimum values. Both Rov 0 and Row 2 have a minimum of -5, which is better than Row 1's minimum of -10. Since Row and Row
tied in terms of their minimum valuea, I'll look their potential for higher payoffa. Row has potential maximum 10, while Row has maximum of 5. Therefore, would choose Row 0.
ORetryClaude does not have the ability to run the code it generates yet.Claude Claude can make mistakes. Please double-check responses.
GPT-4o
We are Player Two (Column chooser) We pick column then Player One picks a row
We get the second number from the chosen cell (x, y).
Now we assume Player One picks the row that minimizes our payoff, again we apply maximin, looking at minimum second values per column:
Column 0: (0,0): -10 (1,0): 10 (2,0): 0 Min -10
Column (0,1): 5 (1,1): (2,1): -5 Min -5
Column (0,2): 8 (1,2): -5 (2,2): 5 Min -5
So: Col 0: -10 Col 1: -5 Col -5 Maximin is -5, achieved by Col
26

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Again, break tie with average: Col 1 values: 8, -5, 5 average 2.67 So Column 2 is better.
5, 0, -5 + average Col 2 values:
27

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Reviews:
[{"review_id": "PYYMdW2lHN", "reviewer": "Reviewer_7W8V", "summary": "This paper brings together two compelling threads—large language models (LLMs) and Behavioral Game Theory—by proposing a unified evaluation framework to assess strategic reasoning and social responsiveness. The authors validate their framework through a broad suite of experiments and conclude with a discussion of limitations and broader impacts.", "questions": "1. Given the identified alignment and reasoning-depth gaps, do you plan to introduce targeted innovations —such as alignment fine-tuning or auxiliary loss functions—to address these challenges in future work?\n2. Considering that the contribution centers on proposing and validating an evaluation framework (without novel algorithmic contributions), have you considered submitting to NeurIPS Datasets & Benchmarks track instead of the main conference?", "limitations": "yes", "rating": 4, "confidence": 2, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "## Strengths ：\n1.The proposed evaluation framework offers a unique bridge between LLM-based reasoning and behavioral game-theoretic analysis. Its theoretical foundations are well articulated, and the framework’s structure shows promise for applications in agentic strategic assessment.\n2.The experimental design is comprehensive: multiple game settings, a diverse range of contemporary models, and fine-grained metrics are employed. This breadth ensures that the framework captures both performance and timeliness in evaluating reasoning depth.\n3.The Social Effect with Human is thoughtfully executed, providing empirical insights. \n\n## Weaknesses：\n1.The paper reads like a combination of two largely independent studies, an evaluation framework and a human-centered social experiment. The narrative would benefit from tighter coupling, illustrating how the evaluation results directly inform or motivate the social effect findings.\n2.While the experimental findings are well presented, the paper lacks proposed innovations to address observed shortcomings. \n3. Since NeurIPS has a benchmark track, I am wondering if such paper should be submitted to the main track.", "was_revised": true, "final_justification": "Considering the comprehensiveness of the empirical study and authors' justifications during rebuttal, I would like to increase my rating. But to be honest, I am not so confident at my evaluation so I will lower my confidence score.", "rebuttal": "Thank you for the review. Below are our responses to your questions and comments. \n\n\n\n\n**Weakness 1 Response:** \n\nThe paper presents a two-stage study, but not just a combination of two separate experiments. The “social effect” study is not an independent effort, but a direct extension and application of our evaluation framework to real-world, human-centered challenges. It should be viewed as the second stage of the same framework:\n\n\n    Stage 1: We use TQRE to estimate each model’s intrinsic reasoning depth, establishing a behavioral baseline.\n    Stage 2: We enhance the estimation through introducing demographic personas or human factors, allowing us to isolate and diagnose how social cues shift model reasoning and expose demographic biases\nThis staged approach demonstrates that an effective evaluation framework must move beyond quantitative performance alone to explicitly address the social and ethical dimensions of agentic reasoning.\nWe can further clarify this linkage more accessible in a revision, making explicit how the social study is motivated by and only made possible through the unified framework introduced earlier.\n\n\n**Weakness 2 Response:** \n\n\nWe adapt TQRE from behavioral economics and show that our framework completely subsumes NE and CH baselines. We emphasize that methodological innovation at this level of breadth and rigor constitutes a major scientific contribution. To our knowledge, no prior work has introduced a comprehensive methodology and extensive quantitative evaluation of LLM reasoning through the behavioral decision-theory lens. Our framework addresses major shortcomings of previous work, such as restrictive or unrealistic assumptions, by offering a rigorous, behavioral approach that directly quantifies reasoning depth and social effects.\nThe issue of improving reasoning depth and alignment across diverse scenarios is a broad, ongoing challenge faced by the entire field, including leading research labs and companies. Our work provides, for the first time, a rigorous and quantitative behavioral lens to measure and compare reasoning depth, laying the necessary foundation for any principled model improvements in the future.\n\nBy exposing and quantifying these limitations in a systematic and interpretable way, our framework enables future work on targeted interventions (e.g., model fine-tuning, training data augmentation, loss function design). We explicitly outline these next steps in our discussion section. Thus, we view our methodological innovation and actionable diagnostics as a crucial advance, enabling and accelerating broader progress on the open problems highlighted by the reviewer. Finding a single solution that aligns all models with one particular reasoning process or style remains a significant challenge. Aligning with one direction sometimes means misaligning with other directions; our framework’s value shows up at where the alignment or misalignment is, but aligning the model with a corresponding target is out of the scope of this work. But of course, we are looking forward to designing methodologies to achieve the ultimate alignment in the future based on the foundation established by this work. \n\n\n**Weakness 3 Response:** \n\nOur work goes beyond a dataset or static benchmark by providing new metrics and theoretical synthesis: it introduces a theoretically grounded, behavioral game-theoretic approach for analyzing LLMs as reasoning agents, including both the modeling methodology and actionable diagnostic tools for both developers and theorists. Moreover, we do not simply report scores, but interpret mechanisms of reasoning, model variation, and real-world alignment/fairness risks. This framework serves as a practical diagnostic tool that enables and facilitates researchers to iterate on LLM studies. These aligned with the NeurIPS main track’s goals of advancing both scientific understanding and practical impact in AI. \n\nSpecifically, we submitted to the main NeurIPS track under the subsection **“Social and economic aspects of machine learning (e.g., fairness, interpretability, human-AI interaction, privacy, safety, strategic behavior)”**. Our work provides a methodological and empirical contribution at the intersection of strategic reasoning, human-AI interaction, and fairness in LLMs, all of which are central themes listed in this track. For these reasons, we believe our paper is a perfect fit for this subsection of the main track, rather than the datasets & benchmarks track. \n\n\n**Question 1 Response:** \n\nYes, these are promising future directions. Our findings directly inform future directions in model improvement and lay the foundations for that. \n\nFor example, the behavioral metrics produced by our framework allow for targeted fine-tuning to improve reasoning depth in specific game types, as well as the identification and mitigation of social biases via curated data augmentation. We are actively exploring these possibilities and believe our framework can serve as a foundation for iterative cycles of evaluation and model alignment. We see this as an important next step.\n\n\n\n**Question 2 Response:** \n\nThis has been answered above in the weakness 3 response."}, {"review_id": "KjbTwoQiZT", "reviewer": "Reviewer_jSzb", "summary": "This paper presents a framework to evaluate the strategic reasoning of LLMs. The authors use a concept from behavioral game theory called Truncated Quantal Response Equilibrium (TQRE) to assess how deeply LLMs think when playing different games. The study tests 22 LLMs to analyze their performance and reasoning styles. It also examines how assigning demographic personas to LLMs changes their strategic choices, highlighting potential biases in model behavior.", "questions": "**1**. You use the TQRE model to estimate reasoning depth. However, your conclusions about how a model reasons (e.g., using a \"minimax\" strategy) seem to come from analyzing the text generated by the model, not from the value itself. Could you explain the direct link between quantitative results with particular reasoning style? \n\n**2**. In Section 4.2, you identify reasoning styles by analyzing excerpts from the models' outputs. This process can be subjective, as it depends on the researcher's interpretation of selected text. Did you use any methods to ensure the consistency and reliability of this analysis?\n\n**3**. You observe that shorter reasoning chains can lead to better performance, which is an interesting finding. However, this analysis appears to be focused on only three top-performing models. How can you be sure this conclusion is generalizable to a wider range of LLMs? The current evidence seems insufficient to support such a broad claim.\n\n**4**. The TQRE model estimates two parameters: reasoning depth $\\tau$ and decision noise $\\gamma$. The paper focuses entirely on the former. Could you please clarify why the $\\gamma$ parameter was excluded from the analysis? Does this parameter provide important information about a model's consistency in decision-making?", "limitations": "yes", "rating": 5, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 4, "strengths_and_weaknesses": "The main strength of this work is its novel approach to evaluating LLMs. Instead of using simple benchmarks, it applies a structured model from behavioral game theory. The method allows the authors to measure a specific metric, reasoning depth $\\tau$, which is effective to quantify strategic thinking. The investigation into how demographic personas affect LLM decisions is also a significant and timely contribution.\n\nHowever, the paper has several key weaknesses. First, the connection between the quantitative $\\tau$ and the qualitative findings (the described reasoning styles) is not clear. The paper does not sufficiently explain how the TQRE model's outputs directly support the conclusions about how models reason. Second, the qualitative analysis of reasoning styles, such as \"minimax,\" is based on selected model outputs, which introduces potential subjectivity. Finally, some of the broader claims, such as those about the effectiveness of Chain-of-Thought (CoT) prompting, are based on a small sample of top-performing models and may not apply to all LLMs.", "was_revised": true, "final_justification": "This paper's core strength lies in its originality and significance, as it introduces an interpretable metric for strategic reasoning. Given that my key reservations have been thoroughly addressed, I now believe the reasons to accept this paper outweigh any remaining limitations.", "rebuttal": "Thank you for the review. Below are our responses to your questions and comments. \n\n\n**Question 1 and Weakness 1 (about the link between quantitative reasoning depth and qualitative reasoning styles) Response:** \n\nThis is a very insightful question. Our submission in this “social and economic aspects of machine learning” track has adopted a combined method that is typical in social science research: \n\n    Quantitative layer: A data-driven method, let the data tell the story from the observed behaviors, therefore effectively capturing the underlying mechanism and patterns of the agent. Here, we use TQRE as a rigorous, behavioral metric to quantify how deeply each LLM appears to reason in strategic settings. \n\n    Qualitative layer: To complement the quantitative analysis, we mirror the “verbal protocol analysis”, which is a well-established qualitative method in the behavioral sciences. Specifically, each CoT trace generated by the model is treated as an “interview transcript,” and we conduct thematic coding using a pre‑defined rubric, which is a qualitative analysis method for systematically labeling and organizing recurring ideas or patterns in qualitative data, such as text or transcripts (Braun & Clarke, 2006), to identify reasoning styles.\n\nThis qualitative layer is essential because, just as with human agents, numbers alone rarely reveal the full narrative or structure of reasoning, and a contextual “story” is needed to interpret the meaning of quantitative signals. The linkage, therefore, is methodological rather than algebraic: the quantitative TQRE analysis tells us how far the agent seems to think; the qualitative “interview” reveals how it uses that depth. \n\nEmploying both layers is standard practice when behavioural‑decision research aims to connect statistical regularities with interpretive understanding, and it is precisely this synthesis that our framework contributes to LLM evaluation. We will revise the text to make it clearer how this synthetic approach works. \n\n\n**Question 2 and Weakness 2 (about the method to avoid subjectivity and keep reliability) Response:** \n\nYes, thank you for asking. We took the following steps to ensure the robustness and avoid subjectivity: We collected a diverse set of reasoning traces from different models and anonymized them before analysis. The researchers who coded each CoT trace for reasoning style did so without knowing which model produced it, analogous to a “blind review” process. This helps to minimize potential post-hoc bias. We then used a pre-defined structured coding rubric to classify reasoning styles. \n\nThen we did the cross-validation to mitigate subjectivity. Multiple researchers independently coded overlapping subsets of the data, and we compared their classifications to check for consistency. \n\n**Question 3 Response:** \n\nOur conclusion is not necessarily that “shorter chains are always better”, but that the common assumption “longer CoT → better strategic reasoning” does not always hold true. Therefore, the main takeaway is that the researchers should measure, but not assume the effect of CoT length. \n\n\n**Question 4 Response:** \n\nIn our analysis, we focused primarily on τ because it is the key metric for strategic sophistication in behavioral game theory, as it directly reflects the depth of recursive reasoning and belief modeling. The γ parameter (decision noise), on the other hand, primarily serves as a control variable. It accounts for contextual confounders within the experimental setup and helps ensure the robustness of our primary measure τ. γ did not provide a consistent, model-wide insight comparable to τ, and due to page limit, we didn’t focus on discussing it and left more space to make the major objective clearer. Nevertheless, we acknowledge the reviewer’s suggestion and will include a detailed summary of γ values in the appendix of the revised paper. For reference, we have provided a table of γ estimates here. \n\n| Scenario | claude-3 | deepseek 2.5 | deepseek r1 | gemini 2.0 | gemma | gpt 4o | gpt o1 | gpt o3 mini | internlm 2.5 | LLAMA 405B | Llama 8B | Qwen 32 B |\n| :--- | ---: | ---: | ---: | ---: | ---: | ---: | ---: | ---: | ---: | ---: | ---: | ---: |\n| competitive | 5.833 | 7.669 | 11.383 | 1.719 | 8.834 | 2.053 | 0.441 | 1.131 | 5.384 | 6.154 | 0.000 | 0.370 |\n| cooperation | 1.687 | 3.347 | 0.348 | 2.009 | 0.348 | 1.667 | 3.349 | 3.347 | 1.667 | 1.667 | 0.336 | 1.696 |\n| Incomplete-Bayesian-p05 | 5.000 | 5.001 | 0.000 | 5.001 | 0.031 | 0.846 | 5.001 | 5.001 | 0.000 | 0.025 | 0.337 | 6.609 |\n| Incomplete-Bayesian-p09 | 5.276 | 5.276 | 0.014 | 5.276 | 0.317 | 0.950 | 5.276 | 5.276 | 0.593 | 0.441 | 5.861 | 0.842 |\n| Incomplete-Signaling | 0.355 | 0.120 | 0.156 | 0.300 | 0.129 | 0.236 | 0.395 | 0.120 | 0.061 | 0.000 | 0.081 | 0.882 |\n| mix motive | 0.000 | 1.711 | 0.000 | 0.348 | 0.000 | 0.000 | 3.717 | 1.720 | 0.000 | 0.000 | 0.000 | 1.813 |\n| Sequential | 38.675 | 52.656 | 40.615 | 0.000 | 52.362 | 34.198 | 0.676 | 35.734 | 42.306 | 37.102 | 48.384 | 48.972 |\n|   |   |   |   |   |   |   |   |   |   |   |   |   |\n\n**Weakness 3 Response:**\n\nIn illustrating how our unified framework combines qualitative and quantitative methods, we focused our deeper analysis mainly on top-performing models for several reasons: (1) these models consistently provide explicit internal reasoning steps (Chain-of-Thought traces), whereas many smaller or less capable models do not provide reasoning steps as an API feature; and (2) as top performers, their behavior offers stronger and more discernible features, making trends more interpretable. For example, while many intermediate models perform moderately across games, the three models we selected demonstrate clear strengths and weaknesses (e.g., DeepSeek R1 excels in cooperative games but underperforms elsewhere), making it more intuitive to link reasoning patterns to their successes and failures. However, studies and results about lower-performing models are also included in the paper in section 4.3. We will elaborate more about those parts in the final version. \n\nWe do not claim that the observed effects of CoT prompting are universal across all LLMs; indeed, each model exhibits its own reasoning style and behavioral pattern. Rather, our goal is to demonstrate that the unified framework can reveal these trends within individual models, particularly where reasoning traces are available and informative. We will clarify this point and its limitations in the revised manuscript as well. \n\n**Reference:**\n\nBraun, V., & Clarke, V. (2006). Using thematic analysis in psychology. Qualitative Research in Psychology, 3(2), 77–101."}, {"review_id": "2KcRRvitjs", "reviewer": "Reviewer_aEWT", "summary": "This paper presents a framework for evaluating the strategic reasoning capabilities of Large Language Models (LLMs) when they act as agents in interactive scenarios. The authors argue that traditional evaluation methods, often based on Nash Equilibrium (NE), are insufficient as they overlook the bounded rationality and stochasticity inherent in LLM decision-making. To address this gap, the paper introduces an evaluation framework grounded in behavioral game theory.\n\nThe core of the methodology is the application of the Truncated Quantal Response Equilibrium (TQRE) model to analyze LLM behavior across a diverse library of 13 strategic games. By fitting the TQRE model to the observed choices of 22 state-of-the-art LLMs, the framework estimates a key parameter, τ, which quantifies the depth of strategic reasoning for each model. The study further investigates how reasoning capabilities are influenced by Chain-of-Thought (CoT) prompting and the assignment of demographic personas. The key findings are threefold: (1) Reasoning depth varies significantly across models and is not solely determined by model size; (2) Different models exhibit distinct reasoning styles (e.g., maximin, belief-based); and (3) LLMs display context-sensitive shifts in reasoning and potential social biases when assigned demographic identities.", "questions": "I would be willing to raise my score if the authors could elaborate on the following points.\n\n- The analysis of dominant reasoning styles is fascinating. Are these styles stable, intrinsic properties of the LLMs, or are they highly context-dependent? For example, would a model like GPT-01, which shows a strong maximin preference, adapt its style in a game with more cooperative elements or under prompts that encourage trust? A deeper exploration of the malleability of these styles would be very insightful.\n- The discovery of reasoning shifts based on demographic personas is a critical finding. The paper shows that it happens, but the why remains an open question. Do the authors have a hypothesis regarding the mechanism? Is it primarily a reflection of statistical biases in the training data (e.g., text corpora associating certain demographics with certain behaviors), or could the RLHF process also play a role in shaping these context-dependent responses?\n- The framework estimates both τ (depth) and γ (precision/noise). The main analysis focuses on τ. Is there any interesting correlation or trade-off between τ and γ across models? For instance, do models with deeper reasoning also tend to be less noisy (higher γ)? Did the persona-based prompts also cause significant shifts in γ, which could distinguish between a change in \"cognitive ability\" versus a change in \"decision consistency\"?\n- The qualitative analysis relies on the reasoning chains (CoT) generated by the models. How confident can we be that these chains accurately reflect the model's \"true\" internal reasoning process, rather than being a post-hoc rationalization of a decision reached through other means? While this is a notoriously difficult problem, a brief discussion of this caveat would add to the paper's rigor.", "limitations": "The authors have included a \"Limitations and Future Directions\" section, which is commendable. To re-emphasize and structure these points:\n- L1: Focus on One-Shot, Static Games: As mentioned, the current framework is designed for and evaluated on static, normal-form games. Its direct application to dynamic, extensive-form games where the game state evolves and players' histories matter is a non-trivial extension and a key limitation of the current work's scope.\n- L2: Causality of Prompting Effects: The paper demonstrates strong correlations between prompts (CoT, personas) and changes in reasoning behavior. However, as the authors note, establishing a clear causal link remains an open challenge. The \"why\" behind these effects is not fully explained by the current framework.\n- L3: Semi-Dynamic Framework: The current evaluation is \"semi-dynamic\" as it tests pre-trained models. Extending the framework to analyze real-time multi-agent interactions, where LLMs learn and adapt to each other over multiple rounds, is a significant future step and a limitation of the current static analysis.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "**Strengths:**\n- The introduction of a new paradigm for evaluating LLM strategic reasoning. Moving beyond the binary pass/fail assessment of Nash Equilibrium, the framework provides a continuous, quantitative metric (τ) for reasoning depth, which is grounded in cognitive science from behavioral game theory. This allows for a more interpretable, and fine-grained analysis of LLM capabilities.\n- The paper is  well-written, making complex concepts from behavioral game theory accessible to a broader machine learning audience. The research provides a potentially useful tool for researchers and practitioners to audit and understand LLM behavior in interactive settings.\n\n**Weaknesses:**\n\n- Reliance on a Specific Behavioral Model (TQRE): The entire framework's quantitative conclusions are predicated on the Truncated Quantal Response Equilibrium (TQRE) model. While TQRE is a well-established model in behavioral economics, the paper's findings are inherently conditional on its assumptions (e.g., Poisson-distributed reasoning levels). The work could be strengthened by acknowledging this model-dependency more explicitly and perhaps discussing how results might change under alternative behavioral models (e.g., Cognitive Hierarchy with different belief formation rules).\n- Limited Scope of Interaction: The study focuses exclusively on one-shot, normal-form (matrix) games. This is a deliberate and effective choice for isolating initial strategic reasoning. However, it does not capture the complexities of dynamic, multi-stage interactions where learning, adaptation, reputation, and state evolution play critical roles. This limits the direct generalizability of the specific τ values to more complex, extensive-form games.", "was_revised": true, "final_justification": "After engaging in a thorough and productive discussion with the authors, I have decided to raise my score to \"Borderline Accept\". My decision is primarily driven by the paper's originality and its potential to establish a new paradigm for evaluating strategic reasoning in Large Language Models.\n\nThe primary strength of this work is its pioneering contribution. It moves beyond traditional, often rigid, evaluation metrics by introducing a sophisticated framework grounded in behavioral game theory. The TQRE model and the resulting τ (reasoning depth) metric offer a nuanced, interpretable, and quantitative way to assess LLM behavior. \n\nThrough our discussions, several of my initial concerns were effectively addressed. The authors clarified that the Chain-of-Thought (CoT) analyses are based on concurrent reasoning traces, not post-hoc rationalizations, which strengthens the validity of their qualitative findings. They also provided a well-reasoned argument for the theoretical standing of the TQRE model within the broader family of behavioral models, justifying its selection as a foundational element of their framework.\n\nWhile the current framework is robust, I believe future iterations could be further enriched. For instance, a deeper dive into the γ (precision/noise) parameter could uncover additional layers of insight into decision consistency, providing a valuable complement to the current focus on reasoning depth. Likewise, while the theoretical justification for TQRE is strong, supplementing it with direct empirical model comparisons on LLM-generated data would offer the most conclusive validation for its application in this novel domain.\n\nIn my final assessment, I assign the greatest weight to the foundational value and forward-looking impact of this research. The paper provides a framework to understand the 'what' and 'why' of LLM strategic behavior, which is a contribution before the community can effectively address the 'how' of improving it. For this reason, I believe the compelling reasons to accept this paper, centered on its novelty and foundational significance, now outweigh these remaining areas for future methodological refinement.", "rebuttal": "Thank you for the review. Below are our responses to your questions and comments. \n\n\n\n\n**Question 1 Response:** \n\nOur experiments suggest that dominant reasoning styles are often intrinsic and stable properties of the LLMs we tested. As you mentioned in the question, GPT-o1’s strong maximin preference remains the dominant pattern across most of the 13 games in our library, regardless of specific game context. This intrinsic tendency also explains why GPT-o1 tends to underperform in cooperative or mixed-motive games; it still chooses the secure but collectively inferior outcome. \n\nOur goal is to benchmark the models’ native strategic reasoning. Supplying detailed guidance would blur that line, turning the task into “follow‑the‑instructions” rather than revealing the model’s default reasoning style. We therefore keep prompts minimal and identical across models.\n\n\n**Question 2 Response:** \n\nThanks for bringing up this question. We acknowledge this as an important and interesting problem. The proprietary training corpora and RLHF pipelines of most models are opaque, so we cannot trace a single, provable cause directly.  Any updates to the weights of the model can and will introduce bias to the model’s behavior, and it is quite difficult to pinpoint where the bias is introduced. What we can say, based on our additional “internal‑thinking” audit, is the following:\n\n\n    If we ask the model directly, “Will you treat personas differently?” it would most likely deny the answer. However, the observation would still show the shifts in responses. This suggests that this bias is internal and implicit. \n    \n    The most plausible hypothesis is that large-scale text corpora encode stereotypical associations between demographic and behavioral cues. These priors affect downstream decisions even though the explicit request to the model or its rationale is “to be fair”. For example, some cultures have an emphasis on unity and moderation, so the model trained heavily using data in those regions might benefit more from a cooperation game, such as Deepseek. RLHF can either dampen or amplify these latent patterns by bringing researchers’ personal “preferences”. Without access to the non-public data, it’s hard to disentangle these factors.\n\n\nThe aim of this work is therefore not to locate the ultimate cause of the bias, but to demonstrate that the framework is sensitive and robust enough to reveal such latent biases, even when these trends are absent from the models’ verbal justification.   \n\n**Question 3 Response:** \n\nIn our analysis, we primarily focus on τ as it directly captures strategic reasoning depth, which is central to our study. γ, on the other hand, is included mainly as a control variable to account for variability and contextual confounders in decision-making. We will add further clarification to the final draft. \n\nRegarding the correlation or trade-off between τ and γ, we did not observe any strong or consistent patterns across models or games in our results, and our data does not support a simple relationship or trade-off between these parameters. Since γ did not reveal consistent or generalizable patterns across models, we chose to focus our main discussion on τ in order to maintain clarity and prioritize our primary research objectives within the available space. We thank the reviewer for highlighting this interesting question, and we will consider a deeper analysis of more complex relationships between these two parameters in future work.\n\n**Question 4 Response:** \n\nThe reasoning chains were obtained directly from the model outputs using the API feature that returns the model’s internal step-by-step reasoning for each decision, rather than asking for an explanation after the fact. This process is analogous to revealing the model’s “thought process” as it happens, so it’s not a post-hoc response. Thank you for raising that up, and we will add a note to the paper to make this point clearer. \n\n**Weakness 1 Response:** \n\nOur quantitative framework is grounded in TQRE because, in comparative studies such as Wright & Leyton-Brown (2010, AAAI), it has been shown to fit human data better than alternative models—including Cognitive Hierarchy and standard Quantal Response Equilibrium. \n\nTQRE is closely related to the CH family of models, which can include a variety of belief formation rules. Our use of the Poisson distribution in TQRE follows both theoretical precedent and empirical findings that most agents reason at lower levels, with fewer at higher depths (Camerer, Ho, & Chong, 2004; Costa-Gomes, Crawford, & Broseta, 2001; Stahl & Wilson, 1994, 1995). \n\nWe will discuss how future work could incorporate and compare alternative models into the final draft. Thank you for the suggestion.\n\n**Weakness 2 Response:** \n\nOur methodological choice is grounded in the perspective that dynamic, multi-stage interactions can be decomposed into rounds of one-shot decisions, with each round representing a cross-sectional snapshot of agent reasoning given the available information at that stage.\n\nFor example, consider a multi-round coordination game:\n\nIn the first round, agents have no history or prior information about each other, so they make decisions based solely on the game’s structure and any available cues, just the same as in the one-shot coordination game. In the second round and beyond, agents update their beliefs based on observed past actions. These historical interactions then become part of the information available for subsequent decisions. Thus, each new round can still mirror as a one-shot decision, but conditioned on a richer informational context. \n\n\n\n**Reference:**\n\nWright, J., & Leyton-Brown, K. (2010, July). Beyond equilibrium: Predicting human behavior in normal-form games. In Proceedings of the AAAI Conference on Artificial Intelligence (Vol. 24, No. 1, pp. 901–907).\n\nCamerer, C. F., Ho, T.-H., & Chong, J.-K. (2004). A cognitive hierarchy model of games. Quarterly Journal of Economics, 119(3), 861–898.\n\nCosta-Gomes, M. A., Crawford, V. P., & Broseta, B. (2001). Cognition and behavior in normal-form games: An experimental study. Econometrica, 69(5), 1193–1235.\n\nStahl, D. O., & Wilson, P. W. (1994). Experimental evidence on players' models of other players. Journal of Economic Behavior & Organization, 25(3), 309–327.\n\nStahl, D. O., & Wilson, P. W. (1995). On players' models of other players: Theory and experimental evidence. Games and Economic Behavior, 10(1), 218–254."}, {"review_id": "ztAaCBhBEp", "reviewer": "Reviewer_RAu2", "summary": "This paper introduces a behavioral game-theoretic framework to evaluate the strategic reasoning capabilities of large language models (LLMs). Moving beyond traditional Nash Equilibrium (NE) benchmarks, the authors apply a Truncated Quantal Response Equilibrium (TQRE) model to estimate the reasoning depth (τ) of 22 state-of-the-art LLMs across 13 one-shot matrix games, including competitive, cooperative, mixed-motive, and belief-based games. Results show that reasoning depth varies not only across models and game types but also depends on reasoning styles and context. Chain-of-thought (CoT) analysis reveals that longer reasoning does not always imply better decisions. Furthermore, embedding demographic personas affects performance, with some models exhibiting bias when assigned minority identities. Overall, the study highlights that strategic decision-making in LLMs is shaped by both architecture and prompt context, and that performance alone is not sufficient to ensure fairness or human-aligned behavior.", "questions": "A question that’s closely related—but perhaps beyond the current scope of the paper—is whether the **τ parameter systematically varies with the complexity of the task structure**. From the provided tables, it appears that τ does differ across tasks. However, a deeper and more important question is: **does each model exhibit consistent behavioral adaptation across task types**? That is, does a model tend to use simpler inference in simpler games, and engage in deeper reasoning when the task demands it? And is this reflected in its τ estimates across contexts?\n\nAnswering this would be critical for understanding whether a model’s strategic reasoning is **generalizable and context-sensitive**, or merely a reflection of **fixed priors shaped by uneven training exposure**. If the model truly possesses adaptable reasoning capabilities, we should see its behavior align with the structural demands of different tasks. Otherwise, its performance may just reflect biases in pretraining, rather than a principled ability to engage in strategic thinking.", "limitations": "Yes.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 4, "significance": 3, "originality": 3, "strengths_and_weaknesses": "### **Strengths**\n- This paper introduces a diverse and representative set of LLMs and tasks from game theory (e.g., complete vs. incomplete information, cooperative vs. competitive vs. sequential). The evaluation setup is comprehensive and covers a wide range of strategic scenarios.  \n- The theoretical foundation and modeling framework are solid. The use of TQRE to estimate each model’s reasoning depth (τ) from one-shot behavior is well-motivated and connects nicely to behavioral game theory.  \n- I also appreciate the ethical and demographic analyses. The study probes how demographic prompts (e.g., gender, sexuality) affect strategic behavior, which raises important implications for fairness, bias, and safe AI deployment in interactive settings.\n\n### **Weaknesses**\n- I’m a bit skeptical about interpreting the τ parameter strictly as “reasoning depth.” While the framework is theoretically sound, the evaluation is entirely based on one-shot decisions. That means the models are relying on prior knowledge or inductive biases, not adapting to opponents. So instead of saying one model reasons more deeply than another, I’d frame it as *being biased toward deeper recursion by default*. Without interaction or adaptation, it’s hard to claim that actual recursive reasoning is happening.  \n- Another limitation is that the paper focuses mostly on behavioral outcomes. The chain-of-thought (CoT) content is only lightly touched upon. Since recursive reasoning could be more directly observable in the CoT traces, a more systematic analysis there would strengthen the claims. For example, parsing the CoTs for syntactic recursion, or using an LLM-as-judge to label reasoning levels, could reveal whether verbal reasoning depth aligns with behavioral τ. This would help ground the τ measure and improve interpretability.\n- Another missing point is the authors did not report how well the models (TQRE) fit to each LLM's behaviors (as well as in a diverse of tasks). Without knowing how well the TQRE model explains the behaviors of LLMs, it's hard to tell convinceness of the tau estimation. Another one is to figure out whether TQRE is always the best model to explain the LLM's behaviors. The authors should prepare some classical behavioral game theory or theory of mind models for testing against TQRE. Those model comparison and goodness-of-fit metrics would help to improve the convinceness of the parameter results.", "was_revised": true, "final_justification": "The authors partially addressed my concerns about empirical evidence and I would like to increase my rating to 4 to support the quality and originality of the paper.", "rebuttal": "Thank you for the review. Below are our responses to your questions and comments. \n\n\n\n\n**Weakness 1 Response:** \n\nThe concept of reasoning depth (sometimes also referred to as “levels of reasoning” or “strategic sophistication”) is a longstanding and standard practice in behavioral game theory and experimental economics. Classic works (e.g., Camerer, Ho, & Chong 2004; Costa-Gomes, Crawford, & Broseta 2001; Wright & Leyton-Brown 2010) use one-shot games specifically to benchmark and quantify these capacities.\n\nSecondly, dynamic, multi-stage interactions are commonly analyzed as sequences of one-shot decisions, each defined by the agent’s reasoning given the available information at that stage. This decomposition is a standard approach in game theory and behavioral economics (Camerer 2003; Fudenberg & Tirole 1991), where each round is modeled as a one-shot decision conditioned on the current information set. Similar to current practice with LLMs, multi‑round analyses are implemented by appending the transcript of each preceding round to the prompt, allowing the model to revise its decisions and adapt to its opponent. From the LLM’s perspective, a dynamic strategic game thus remains a single‑shot decision problem presented within an ever‑growing context window. Although the model’s finite context length eventually limits how many rounds can be accommodated, this constraint does not undermine our framework: the core evaluation metric, reasoning depth, captures the model’s capabilities across all relevant dimensions and therefore remains valid regardless of prompt length. \n\nAdaptation and learning over repeated play are valuable research avenues, but they differ from the baseline strategic reasoning that our framework measures. Recursive reasoning asks, “How many steps ahead can the agent think, given its priors?” Learning dynamics ask, “How efficiently and quickly can it update those priors?” Our framework targets the former. Moreover, whether the agent relies on innate priors or on newly acquired knowledge of the game, its “thinking paradigm” remains the same.\n\n\n\n**Weakness 2 Response:** \n\nThanks for the suggestions. Adding comparison using syntactic recursion for CoT parsing or using LLM-as-judge are promising ideas, and we will definitely consider them in our ongoing and future studies. Nonetheless, we want to point out that we opted for experienced human annotators in the current study for greater interpretability and established validity, and because there is currently no robust evidence that LLMs can accurately or validly assess the reasoning depth of other LLMs. Employing LLMs as judges would require substantial new validation and would shift the focus of our work away from behavioral evaluation and interpretability. In current work, using LLMs to judge other LLMs is challenging also because it could introduce circular logic, as both may share training data, inductive biases, or flaws. We agree that using additional analysis is value-added, but it can only be considered as parallel analysis. \n\nCoT is a major focus of our work. In this work, we systematically collected diverse reasoning traces from each model and anonymized them for “blind review.” Our researchers independently classified the reasoning styles using a structured coding rubric, with cross-validation to ensure reliability. The procedure directly links behavioral patterns (e.g., “self-interested” or “distrustful” models struggling to cooperate) to CoT explanations. Please check Section 4.2 for more details. \n\nWe are happy to include your proposed judges for comparison. \n  \n\n**Weakness 3 Response:** \n\nThere might be a misunderstanding here. The TQRE model used in our analysis is not a data-driven machine learning model, but a well-established structural model from behavioral economics and experimental game theory. TQRE does not “learn” its parameters from the data in a flexible way, but rather imposes a theoretically motivated structure to interpret observed choices, which is an approach widely used for both human and agent behavior. If you are referring to the maximum log likelihood of TQRE fits, for individual models and games, the average negative maximum log likelihood per game is typically in the range of 0–2, which is comparable to prior experimental studies (Camerer, Ho, & Chong, 2004). \n\nWe adapted TQRE as the foundation of our quantitative framework based on rigorous justification. It builds upon and extends earlier behavioral game theory models, such as the Cognitive Hierarchy model families and the Quantal Response Equilibrium models, by incorporating bounded rationality, noisy response, and empirically realistic distributions of reasoning depth. It is already the most comprehensive and realistic model compared to other CH-family and QRE models, as shown in comparative studies (e.g., Wright & Leyton-Brown, 2010, AAAI), to provide the best fit to actual agent behavior. \n\n\n\n**Questions Response:** \n\nWe address precisely this issue in Section 4.2 of our paper, where we analyze model behavior and internal reasoning processes across a diverse set of game types. Our results show that models do exhibit typical patterns in different types of games, and each model tends to have its own areas of strength and weakness given their reasoning styles, and these patterns are reflected in both their behavioral choices and internal chain-of-thought reasoning. \n\nIt is important to recognize that the “task complexity” you refer to is not an absolute measure. For instance, a cooperative game might be straightforward for a model with a preference toward trust, but much more complex for a model that assumes opponents are untrustworthy, requiring more layers of strategic reasoning and anticipation of adversarial play. \n\nThe TQRE framework is specifically designed to accommodate this heterogeneity. Rather than assuming a fixed hierarchy of task difficulty, TQRE estimates τ based on how an agent actually navigates the strategic landscape of each game, given its own reasoning process, beliefs, and biases. This means that an increase in τ for a particular agent in a given game reflects that agent’s need for deeper recursion, and not an externally imposed notion of complexity.\n\nOur findings confirm that models display distinct patterns across game types rather than a universal progression from “simple” to “complex.” This agent-relative perspective is fundamental in behavioral game theory and essential for interpreting τ as a measure of context-sensitive strategic depth.\n\n\n\n\n**Reference:**\n\nWright, J., & Leyton-Brown, K. (2010, July). Beyond equilibrium: Predicting human behavior in normal-form games. In Proceedings of the AAAI Conference on Artificial Intelligence (Vol. 24, No. 1, pp. 901–907).\n\nCamerer, C. F., Ho, T.-H., & Chong, J.-K. (2004). A cognitive hierarchy model of games. Quarterly Journal of Economics, 119(3), 861–898.\n\nCosta-Gomes, M. A., Crawford, V. P., & Broseta, B. (2001). Cognition and behavior in normal-form games: An experimental study. Econometrica, 69(5), 1193–1235."}]

Author rebuttal:

Meta-review: This paper proposes a behavioral game-theoretic framework to assess the strategic reasoning capabilities of large language models (LLMs). Drawing from the Truncated Quantal Response Equilibrium (TQRE) model, it estimates a reasoning depth parameter (τ) for 22 state-of-the-art LLMs across 13 one-shot strategic games, revealing variations in reasoning depth by model, game type, and context. Key findings include: models like GPT-o1-mini, GPT-o1, and DeepSeek-R1 exhibit higher reasoning depth; distinct reasoning styles (e.g., maximin, belief-based) emerge from chain-of-thought (CoT) analysis, where longer chains do not always correlate with better decisions; and demographic personas induce context-sensitive shifts, with some models showing improved reasoning under female identities and diminished performance under minority sexuality cues.

During review & rebuttal, reviewers raised concerns about: (1) the paper's fit for the main track versus benchmarks, addressed by authors emphasizing methodological innovation and social relevance; (2) unclear links between quantitative (τ) and qualitative (CoT styles) analyses, clarified via social science practices like thematic coding; (3) omission of γ analysis, responded to with a table and explanation of its control role; (4) TQRE's suitability for LLMs without model comparisons or fit metrics, justified theoretically as encompassing prior models, with fit data provided; (5) one-shot focus limiting adaptation insights, countered by noting decomposition of dynamics into one-shot decisions. 

Both authors and reviewers engaged actively, with most reviewers raising scores post-discussion.

Overall, I think this paper introduces a rigorous, interpretable framework that advances understanding of agentic behavior, with strong empirical support and implications for fairness and alignment—core to the social aspects track. While not proposing fixes, it provides essential "what" and "why" insights for future improvements.
Decision: Accept (poster)