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

2026-07-29

AI Summary

This work addresses the unpredictable performance of fine-tuned large language models in game-theoretic tasks and the lack of effective explanations for cross-game transfer. The authors propose a lightweight behavioral embedding that captures the intrinsic decision-making demands of normal-form games through Nash equilibrium entropy and best-response sensitivity. This approach reveals, for the first time, that strategy transferability is governed by the behavioral structure of games rather than the geometry of payoff matrices, overcoming the limitation of conventional structural embeddings that merely memorize game identities. Experimental results demonstrate that the proposed embedding reliably predicts model performance shifts on unseen games and significantly outperforms existing methods, thereby validating the central role of behavioral characteristics in strategic transfer.

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.

Problem

• strategic transfer
• large language models
• normal-form games
• behavioral embedding
• Nash equilibrium

Innovation

• behavioural embedding
• normal-form games
• strategic transfer
• Nash equilibrium entropy
• response sensitivity