# Strategy, Not Payoffs: A Behavioural Embedding of Normal-Form Games

arXiv: https://arxiv.org/abs/2607.27536 · HTML: https://mlsanity.com/paper/2607.27536/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 35 references that are in the map.
- First posted on arXiv 30 Jul 2026.

## Builds on (most cited first, 22 of 22)

- [Generative Agents: Interactive Simulacra of Human Behavior](https://mlsanity.com/paper/2304.03442/) (2023)
- [Taskonomy: Disentangling Task Transfer Learning](https://mlsanity.com/paper/1804.08328/) (2018)
- [Playing repeated games with Large Language Models](https://mlsanity.com/paper/2305.16867/) (2023)
- [Task2Vec: Task Embedding for Meta-Learning](https://mlsanity.com/paper/1902.03545/) (2019)
- [LEEP: A New Measure to Evaluate Transferability of Learned Representations](https://mlsanity.com/paper/2002.12462/) (2020)
- [LogME: Practical Assessment of Pre-trained Models for Transfer Learning](https://mlsanity.com/paper/2102.11005/) (2021)
- [Open Problems in Cooperative AI](https://mlsanity.com/paper/2012.08630/) (2020)
- [Geometric Dataset Distances via Optimal Transport](https://mlsanity.com/paper/2002.02923/) (2020)
- [Exploring and Predicting Transferability across NLP Tasks](https://mlsanity.com/paper/2005.00770/) (2020)
- [GTBench: Uncovering the Strategic Reasoning Limitations of LLMs via Game-Theoretic Evaluations](https://mlsanity.com/paper/2402.12348/) (2024)
- [Can Large Language Models Serve as Rational Players in Game Theory? A Systematic Analysis](https://mlsanity.com/paper/2312.05488/) (2023)
- [Strategic Reasoning with Language Models](https://mlsanity.com/paper/2305.19165/) (2023)
- [α-Rank: Multi-Agent Evaluation by Evolution](https://mlsanity.com/paper/1903.01373/) (2019)
- [How stable are Transferability Metrics evaluations?](https://mlsanity.com/paper/2204.01403/) (2022)
- [Steering Language Models with Game-Theoretic Solvers](https://mlsanity.com/paper/2402.01704/) (2024)
- [Empirical Game-Theoretic Analysis: A Survey](https://mlsanity.com/paper/2403.04018/) (2024)
- [Large Model Strategic Thinking, Small Model Efficiency: Transferring Theory of Mind in Large Language Models](https://mlsanity.com/paper/2408.05241/) (2024)
- [Strategic Intelligence in Large Language Models: Evidence from evolutionary Game Theory](https://mlsanity.com/paper/2507.02618/) (2025)
- [Task2Box: Box Embeddings for Modeling Asymmetric Task Relationships](https://mlsanity.com/paper/2403.17173/) (2024)
- [Equilibrium-Invariant Embedding, Metric Space, and Fundamental Set of 2×2 Normal-Form Games](https://mlsanity.com/paper/2304.09978/) (2023)
- [Exploring the Effectiveness and Consistency of Task Selection in Intermediate-Task Transfer Learning](https://mlsanity.com/paper/2407.16245/) (2024)
- [Large language models replicate and predict human cooperation across experiments in game theory](https://mlsanity.com/paper/2511.04500/) (2025)

## Abstract (arXiv)

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.