Choosing LLMs for Strategic Agent Interactions

Arastun Mammadli; Herbert Woisetschläger; Jawad Fayaz; Shiqiang Wang

cs.AIOct 13, 2026

Choosing LLMs for Strategic Agent Interactions

Authors: Arastun Mammadli, Herbert Woisetschläger, Jawad Fayaz, Shiqiang Wang

Organizations: University of Exeter United Kingdom · IBM Research Switzerland

Abstract

Game-theoretic benchmarks claim that large language model (LLM) strategic decision-making varies across game types, interaction structures, and capability dimensions. However, they only evaluate strategic performance across individual fixed models. In parallel, contemporary LLM routers pick models under quality-cost trade-offs, but with no notion of a strategic structure. They do not account for an opponent that might be unknown, and that can adapt over time and shift the feedback signal. To address this, we extend the game-theoretic evaluations and define strategic selection as the meta game layered on top of the base game. In each round, a strategic selector fields an LLM from a portfolio of models to navigate a game payoff matrix that is latent and learned online. We find that the evaluation signal is game-specific, and that extracting a reliable signal requires a much higher number of seed runs $N$ compared to traditional benchmarking setups. Evaluating across 5 games and 10 LLMs, we show a model's strategic competence varies significantly depending on the game setup and the opponent faced. Building on this, we implement a suite of selector methods and find that approaches that rely on query embeddings or LLM self-reflection do not consistently capture the underlying strategic signal. A lightweight multi-armed bandit algorithm performs more reliably across games, though it still falls short of the best fixed model. Finally, we show that simple non-stationary and adversarial bandit variants fail to outperform a stationary bandit baseline, pointing to a gap in how current methods handle a shifting opponent in strategic settings.

Figures & tables

Figure 1: Left: A strategic selector $i$ plays a repeated game over $T$ rounds against an unknown opponent $-i$ and observes the game outcome $\xi_{i,t}$ . The $\textsc{Update}(\theta_{i,t},x_{i,t},\xi_{i,t})$ function is applied at every round $t$ . Right: Strategic performance (game utility $v$ ) varies across games and models.

Method	Cost-Aware	Opp.-ID	Online	Embed.	Non-Stat.	Source
Fixed Model	$\times$	$\times$	$\times$	$\times$	$\times$	—
Per-Opponent Full-Information	$\checkmark$	$\checkmark$	$\times$	$\times$	$\times$	—
Implemented selectors
LLM Selector	$\checkmark$	$\times$	$\checkmark$	$\times$	$\times$	Shinn et al. [21]
RouterDC	$\checkmark$	$\times$	$\times$	$\checkmark$	$\times$	Chen et al. [5]
Causal LLM Router	$\checkmark$	$\times$	$\checkmark$	$\checkmark$	$\times$	Tsiourvas et al. [26]

Table 1: Implemented suite of selector methods. Cost-Aware : the method accounts for a quality-cost trade-off when selecting a model. Opp.-ID : the opponent’s identity is revealed to the selector. Online : the method learns online (round-by-round) from game outcomes. Embed. : the method encodes context into embeddings before feeding them into the predictor. Non-Stat. : the method is designed to handle a non-stationary environment.

Panel of Figure 2 — Figure 2: (a) Model scale does not reliably translate into strategic capability. (b) Models differ in strategic disposition. Each point shows a model at the projection of its seven in-game disposition scores onto the first two principal components. Granite , Mistral , Llama , Qwen3.5 .

Model	Chicken Game	Colonel Blotto	Cournot Duopoly	Stag Hunt	Vickrey Auction
Granite4.1 3B	87.5 $\pm$ 0.3	50.6 $\pm$ 0.3	26.0 $\pm$ 1.2	74.3 $\pm$ 2.9	74.3 $\pm$ 0.6
Granite4.1 8B	69.6 $\pm$ 3.0	50.5 $\pm$ 0.3	7.8 $\pm$ 1.5	65.6 $\pm$ 2.2	73.7 $\pm$ 0.6
Granite4.1 30B	87.3 $\pm$ 0.3	50.4 $\pm$ 0.2	13.2 $\pm$ 1.5	72.9 $\pm$ 2.9	69.4 $\pm$ 0.5
Ministral3 3B	86.4 $\pm$ 0.7	48.5 $\pm$ 0.5	18.4 $\pm$ 2.0	73.0 $\pm$ 2.8	72.0 $\pm$ 0.6
Mistral-Nemo 12B	84.2 $\pm$ 1.2	50.3 $\pm$ 0.2	20.0 $\pm$ 2.3	72.7 $\pm$ 2.8	71.9 $\pm$ 0.6
Mistral-Small 3.2 24B	82.2 $\pm$ 1.7	49.7 $\pm$ 0.3	35.2 $\pm$ 2.8	56.1 $\pm$ 1.2	72.5 $\pm$ 0.6

Table 2: Normalised in-game utility

v\uparrow

acquired by each model across 5 games. We report the mean

\pm

95% CI,

\times 100

, aggregated across all pairwise matchups, using

T=1

round,

N=300

seeds per run, and highlight the best score for each game.

Selector	Chicken Game	Colonel Blotto	Cournot Duopoly	Stag Hunt	Vickrey Auction
Reports normalised gain $g$ $\uparrow$
Per-Opponent Full-Information	92.8 $\pm$ 0.4	73.0 $\pm$ 0.2	80.7 $\pm$ 1.5	92.2 $\pm$ 1.0	86.7 $\pm$ 0.5
Thompson Sampler (TS)	85.1 $\pm$ 0.5	71.2 $\pm$ 0.2	47.7 $\pm$ 0.8	76.1 $\pm$ 0.8	74.8 $\pm$ 0.1
RouterDC	84.3 $\pm$ 0.1	68.6 $\pm$ 0.1	36.2 $\pm$ 0.1	74.4 $\pm$ 0.8	72.8 $\pm$ 0.2
Causal LLM Router	78.6 $\pm$ 0.7	63.2 $\pm$ 0.5	31.3 $\pm$ 0.7	74.0 $\pm$ 0.9	64.8 $\pm$ 0.5
LLM Selector	61.0 $\pm$ 0.6	46.9 $\pm$ 0.3	26.9 $\pm$ 0.5	46.6 $\pm$ 1.2	54.4 $\pm$ 0.2

Table 3: Normalised net gain

g\uparrow

(top) and in-game utility

v\uparrow

(bottom) acquired by each selector, against fixed opponents and across 5 games. We show the mean

\pm

95% CI,

\times 100

, averaged across 10 runs (the size of our portfolio), using

T=300

rounds,

N=1

seed per run, and highlight the best score for each game. Selectors’ learning signal was set as their per-round gain

g_{i,t}

Selector	net gain $g$ $\uparrow$	in-game utility $v$ $\uparrow$	usage cost $c$ ( $\times 10^{-3}$ $)$ \downarrow$
Thompson Sampler (TS)	72.4 $\pm$ 0.8	47.1 $\pm$ 1.7	0.027 $\pm$ 0.001
Sliding-Window TS	65.9 $\pm$ 0.7	33.2 $\pm$ 1.4	0.017 $\pm$ 0.001
Discounted TS	63.1 $\pm$ 0.8	27.5 $\pm$ 1.6	0.017 $\pm$ 0.001
EXP3	60.2 $\pm$ 0.7	22.1 $\pm$ 1.4	0.020 $\pm$ 0.001
RouterDC	59.6 $\pm$ 0.3	19.3 $\pm$ 0.5	0.002 $\pm$ 0.000
Causal LLM Router	59.1 $\pm$ 0.7	19.7 $\pm$ 1.3	0.019 $\pm$ 0.001

Table 4: Normalised net gain

g\uparrow

, in-game utility

v\uparrow

, and raw usage cost

c\downarrow

acquired by each selector, against other selectors and in Cournot Duopoly. We report the mean

\pm

95% CI,

\times 100

, aggregated across all pairwise matchups, using

T=300

rounds,

N=1

seed per run, and highlight the best score for each metric. Selectors’ learning signal was set as their per-round gain

g_{i,t}

Appendix figures & tables11 assets

Supplementary material from the paper’s appendix.

Appendix

Symbol	Meaning
Meta Game $\Gamma$ (LLM selection game)
$i,-i$	player indices, where $-i$ denotes the opponent of $i$
$t=1,\dots,T$	round index of the game
$N$	number of seeds in the game (independent replications)
$S_{i}=\{1,\dots,M_{i}\}$	finite set of pure strategies, i.e. player $i$ ’s model portfolio
$\sigma_{i}\in\Delta(S_{i})$	mixed strategy for player $i$ , a probability simplex over $S_{i}$

Appendix

Table A.1 : Glossary of notation.

Panel of Figure 8 — Figure B.1 : Statistical analysis of signal and noise across 5 games and 4 model families. (a) Signal, noise, and SNR per game, $n=300$ . (b) Similar to Heineman et al. [8] $(R=0.79)$ we show that our correlation holds at $r\approx 0.81$ from $n=75$ onwards.

Panel of Figure 9 — Figure B.2 : Statistical analysis of signal and noise across 5 games and 4 model families. (a) Fraction of all 45 reported pairwise gaps that are statistically detectable. (b) Decision accuracy, mean over 30 subsample draws per $n$ .

Model	Hugging Face repository
granite4.1:3b	ibm-granite/granite-4.1-3b
granite4.1:8b	ibm-granite/granite-4.1-8b
granite4.1:30b	ibm-granite/granite-4.1-30b
llama3.1:8b-instruct-q4_K_M	meta-llama/Llama-3.1-8B-Instruct
llama3.3:70b	meta-llama/Llama-3.3-70B-Instruct
ministral-3:3b	mistralai/Ministral-3-3B-Instruct-2512

Appendix

Table C.1 : Model portfolio used across experiments.

Game	Structure	Source
Chicken Game	anti-coordination, brinkmanship	https://en.wikipedia.org/wiki/Chicken_(game)
Colonel Blotto	zero-sum resource allocation	https://en.wikipedia.org/wiki/Blotto_game
Cournot Duopoly	simultaneous quantity competition	https://en.wikipedia.org/wiki/Cournot_competition
Stag Hunt	coordination, risk dominance	https://en.wikipedia.org/wiki/Stag_hunt
Vickrey Auction	second-price sealed-bid auction	https://en.wikipedia.org/wiki/Vickrey_auction

Appendix

Table C.2 : The five base games

\mathcal{G}

used across experiments, all played between 2 players.

Game	Disposition	Definition	PC1	PC2
Chicken Game	Risk appetite	Fraction of rounds choosing dare over swerve.	$\mathbf{+0.35}$	$-0.12$
Cournot Duopoly	Cooperativeness	Collusion index; 1 = joint-profit quantity, 0 = at or beyond Nash.	$\mathbf{-0.45}$	$\mathbf{-0.41}$
Cournot Duopoly	Aggressiveness	Own minus opponent quantity, as a share of the maximum quantity.	$\mathbf{+0.49}$	$\mathbf{+0.35}$
Stag Hunt	Risk appetite	Fraction of rounds choosing stag over the safe hare.	$\mathbf{-0.38}$	$\mathbf{+0.50}$
Stag Hunt	Cooperativeness	Fraction of rounds landing on mutual stag.	$-0.34$	$\mathbf{+0.54}$
Vickrey Auction	Risk appetite	Mean own bid as a share of the maximum bid.	$\mathbf{+0.38}$	$+0.29$

Appendix

Table D.1 : Strategic disposition metrics and their loadings on the first two principal components. All metrics are averaged across rounds and lie in

[0,1]

Figure D.1 : Normalised in-game utility

v\uparrow

against the disposition. Dashed lines show the linear fit and

r

its Pearson correlation. Granite , Mistral , Llama , Qwen3.5 .

Figure D.2 : Strategic dispositions inferred from in-game behaviour for each model family. Each axis is min-max normalised across the 10 models of the portfolio. Granite , Mistral , Llama , Qwen3.5 .

Model	Chicken Game	Colonel Blotto	Cournot Duopoly	Stag Hunt	Vickrey Auction
Reports normalised gain $g$ $\uparrow$
Granite4.1 3B	93.8 $\pm$ 0.1	75.2 $\pm$ 0.1	63.0 $\pm$ 0.6	87.2 $\pm$ 1.4	87.2 $\pm$ 0.3
Granite4.1 8B	82.3 $\pm$ 1.5	74.5 $\pm$ 0.1	46.9 $\pm$ 0.8	72.0 $\pm$ 1.2	85.8 $\pm$ 0.3
Granite4.1 30B	87.0 $\pm$ 0.1	74.0 $\pm$ 0.1	48.6 $\pm$ 0.9	78.1 $\pm$ 1.4	80.1 $\pm$ 0.3
Ministral3 3B	86.5 $\pm$ 0.4	73.4 $\pm$ 0.2	53.5 $\pm$ 1.0	78.2 $\pm$ 1.4	84.2 $\pm$ 0.3
Mistral-Nemo 12B	92.1 $\pm$ 0.6	75.0 $\pm$ 0.1	59.4 $\pm$ 1.2	86.2 $\pm$ 1.4	85.8 $\pm$ 0.3

Appendix

Table D.2 : Net gain, normalised utility, and normalised cost acquired by each model across 5 games. We report the mean

\pm

95% CI,

\times 100

, aggregated across all pairwise matchups, using

T=1

round,

N=300

seeds per run. Highlight marks the best score per game within each metric block.

Figure D.3 : Model elo score (bootstrapped) vs. scale. Granite , Mistral , Llama , Qwen3.5 .

Method	Chicken Game	Colonel Blotto	Cournot Duopoly	Stag Hunt	Vickrey Auction
Reports normalised gain $g$ $\uparrow$
Per-Opponent Full-Information	92.8 $\pm$ 0.4	73.0 $\pm$ 0.2	80.7 $\pm$ 1.5	92.2 $\pm$ 1.0	86.7 $\pm$ 0.5
Granite4.1 3B	89.7 $\pm$ 0.1	71.6 $\pm$ 0.1	64.0 $\pm$ 0.5	89.2 $\pm$ 0.8	83.4 $\pm$ 0.2
Granite4.1 8B	84.5 $\pm$ 0.8	70.5 $\pm$ 0.1	49.8 $\pm$ 0.5	81.1 $\pm$ 0.7	82.0 $\pm$ 0.2
Granite4.1 30B	77.3 $\pm$ 0.1	59.1 $\pm$ 0.1	40.9 $\pm$ 0.5	76.6 $\pm$ 0.8	68.6 $\pm$ 0.2
Ministral3 3B	86.5 $\pm$ 0.2	67.3 $\pm$ 0.2	53.3 $\pm$ 0.7	83.6 $\pm$ 0.8	78.9 $\pm$ 0.2

Appendix

Table D.3 : Normalised net gain

g\uparrow

(top) and in-game utility

v\uparrow

(bottom) acquired by each selector and fixed model from full pairwise matchups against each other, and across 5 games. We show the mean

\pm

95% CI,

\times 100

, using

T=300

rounds,

N=1

seed per run, and highlight the best score for each game. Selectors’ learning signal was set as their per-round gain

g_{i,t}

Model Selection

Model selection chooses models, features, or configurations that balance predictive fit, generalization, complexity, and deployment constraints.

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GENSTRAT: Toward a Science of Strategic Reasoning in Large Language Models

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Open paper AskPDF arXiv

Large language models (LLMs) are increasingly deployed as economic agents in marketplaces, auctions, and bidding settings. Anticipating their behavior in any specific deployment is hard. Existing strategic-reasoning benchmarks evaluate models on fixed canonical games. These benchmarks may saturate as the frontier improves, and they do not allow evaluators to generalize with confidence from benchmark performance to the varied and messy strategic environments that actual deployments involve. We introduce GENSTRAT, which uses procedurally generated strategic environments to address these challenges. Concretely, we generate a distribution of two-player zero-sum imperfect-information card games. The generator can draw fresh games on demand, allowing for evergreen evaluation and resistance to contamination. We pair the game distribution with a capability-profile methodology that decomposes model competence across six axes (state space, temporal depth, information sensitivity, opponent modeling, risk, and brittleness). We also introduce a jaggedness measure of within-distribution smoothness that detects when a model's advantage jumps unpredictably between strategically similar games. We sample 50 benchmark games from a 2,000-game generated pool and evaluate nine frontier and open-weight LLMs in a head-to-head tournament with over 36,000 matches. Newer frontier-tier models score higher on average. Beyond that average, models with near-identical overall strength show qualitatively different capability profiles, and two of the top three leaderboard models (gpt-5 and claude) are noticeably more locally volatile than the third (gemini-3.1-pro), despite being close in overall strength. Together, the capability profile and the jaggedness measure give a deployment-relevant diagnostic that the overall ranking alone cannot provide.

Abstract

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