This work proposes a lightweight two-feature embedding that captures fundamental behavioural demands: the entropy of the Nash equilibrium and the sensitivity of optimal responses to an opponent's action, and shows that this embedding reliably predicts performance changes on held-out games.
Abstract
Learning a strategic task changes more than what is directly taught: fine-tuning on one game can either enhance or degrade an agent's ability to reason in another. Understanding and predicting this transfer of strategic capabilities, however, remains a key challenge for large language models (LLMs). Normal-form games provide an ideal testbed for analyzing this phenomenon, as they feature explicitly defined payoffs and well-characterized equilibrium behaviours. In this work, we investigate whether game embeddings can explain and predict changes in LLM strategic capabilities following fine-tuning across different games. We propose a lightweight two-feature embedding that captures fundamental behavioural demands: the entropy of the Nash equilibrium and the sensitivity of optimal responses to an opponent's action. We show that while existing published structural embeddings primarily memorize game identities and fail to generalize, our behavioural embedding reliably predicts performance changes on held-out games. These results demonstrate that the transfer of strategic capabilities in LLMs is not dictated by the payoff geometry of a game, but by the underlying structure of the decision-making behaviour it requires.
We examine the interplay between ordinal, preference-based solution concepts in games and the long-run behavior of game dynamics, asking in particular to what extent the combinatorial data of a game -- its preference graph -- determine the outcomes of no-regret learning dynamics -- such as follow-the-regularized-leader (FTRL). In one direction, we show that the skeleton of every dynamically stable set (i.e. the set of pure profiles it contains) must also be preferentially stable, that is, it must be closed under profitable deviations. We then ask the converse question: when do preferences determine the long-run behavior of the players'learning dynamics? We begin by showing that preferences characterize asymptotic stability in the case of subgames -- i.e. subsets of pure profiles obtained by restricting players'action sets. Beyond this case however, the equivalence between dynamic and preferential stability collapses: concretely, we construct a three-player game with a preferentially stable set whose span is dynamically unstable, showing in this way that preferences do not suffice as a criterion of dynamic stability. We then bridge this gap via the notion of resilience under aggregate deviations, an easy-to-check payoff-based condition that guarantees asymptotic stability of arbitrary spans of pure strategies.
Omar Abbadi, R. Laraki, P. Mertikopoulos· 1 citation
Cooperation is ubiquitous in both natural and human societies, yet its evolutionary basis remains a major challenge. A long-standing puzzle is whether having more information leads to better decision-making and thus a higher level of cooperation. To address this question, we adopt a recently developed reinforcement learning framework in which individuals learn through trial and error to maximize cumulative rewards - a paradigm that has successfully explained diverse emergent patterns in human behaviors. Specifically, we equip a structured population with the Q-learning algorithm and systematically vary the size of the interactive neighborhood, which serves as a proxy for perceived information. Interestingly, we observe a non-monotonic relationship between cooperation prevalence and neighborhood size in both two-dimensional square lattices and Barabasi-Albert scale-free networks. This inverted U-shaped dependence reveals that an optimal amount of information exists, yielding the highest level of cooperation. Mechanistic analyses show that a moderate neighborhood size enables individuals to strike an optimal balance between information sufficiency and decision-making tractability. This balance allows them to detect reciprocal opportunities while avoiding the deterioration of decision quality due to information overload. Our findings challenge everyday intuition, suggesting that a proper amount of information - not more - is optimal for the emergence of cooperation.
Yi-Hsin Ku, Xin Ou, Jiqiang Zhang et al.· 0 citations
Large language model (LLM) agents increasingly operate in strategic settings where outcomes depend on the actions of other agents. This raises a reliability question: will a model choose consistently when the same incentives are presented through different narratives? We introduce Same Game, Different Story, a benchmark that defines strategic robustness as invariance of model-induced action distributions under payoff-preserving changes in framing. We illustrate the framework through a secondary analysis of published aggregate cooperation rates for GPT-3.5, GPT-4, and LLaMa-2 across four social-dilemma games. The retained comparison covers business and friend-sharing framings, representing 24 model-game-context cells and 7,200 decisions in the source study. Because trial-level data were unavailable, approximate counts were reconstructed from published figures; the resulting estimates are therefore illustrative rather than an exact replication. Under the paper's conservative transformation, pooled strategic robustness is 0.783, and friend-sharing framing increases cooperation by 0.307 relative to business framing. The results indicate that social-relational framing can substantially alter LLM behavior even when the underlying action sets and payoffs remain fixed. Strategic robustness should therefore be evaluated separately from strategic competence, using families of payoff-equivalent prompts rather than a single presentation of a game.
Seyed Pouyan Mousavi Davoudi, Alireza Amiri-Margavi, A. Davodi et al.· 2 citations
Large language model agents deployed without a central controller are often assumed to require communication to coordinate their actions. We ask what remains possible without it: when independent instances of the same model cannot communicate, can they still reason about their counterparts well enough to exceed the standard game-theoretic baseline for uncoordinated play? We introduce a benchmark of one-shot, no-communication games in which each of thirteen language models is told only that its counterparts are running the same model and is evaluated against the Nash equilibrium of the underlying game. In two-player matrix games spanning seven archetypes and two to ten actions per player, two frontier-hosted models consistently exceed their Nash benchmark, approaching the optimal joint outcome in several archetypes, while most open-weight models achieve only partial gains that vary sharply by game structure. Performance degrades substantially in team-based games with four or more interchangeable agents, particularly as the action space grows, suggesting that whatever capability drives self-play gains in dyadic games does not transfer to larger multi-agent teams.
Deborah Sinishaw, Qile Zhu, Edwin Meriaux et al.· 0 citations
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