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This research addresses the gap in current LLM routing by introducing a meta-game framework that evaluates model selection against adaptive, unknown opponents rather than static benchmarks. The study demonstrates that simple non-stationary and adversarial bandit methods often fail to outperform stationary baselines, suggesting that reliable strategic signal extraction requires significantly more seed runs than traditional setups. Ultimately, the findings highlight that a model's strategic competence is highly context-dependent on specific game structures and opponent behaviors, challenging the efficacy of current query-embedding or self-reflection-based selection techniques.
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Choosing LLMs for Strategic Agent Interactions

arXiv3 min read

arXiv:2610.18354v1 Announce Type: new 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.

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.

Artificial Intelligence (cs.AI); Information Retrieval (cs.IR); Multiagent Systems (cs.MA)

I.2.11; I.2.6; H.3.3

arXiv:2610.18354 [cs.AI]

(or arXiv:2610.18354v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2610.18354 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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Full text under the publisher's open licence · 355 words

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