From Natural Language to Extensive-Form Game Representations

2025-01-28

AI Summary

Natural-language game rules are inherently informal and ambiguous, making them unsuitable for direct equilibrium analysis. Method: We propose a two-stage automated modeling framework: (1) leveraging large language models (LLMs) to identify information sets and partial game-tree structures; and (2) integrating context-aware prompting with a self-debugging mechanism to generate complete extensive-form game representations compliant with the PyGambit format. The framework uniformly supports both perfect- and imperfect-information games, and outputs executable game trees compatible with standard equilibrium solvers. Contribution/Results: Our approach achieves end-to-end automatic translation from unstructured rule descriptions to computationally tractable game models—the first such method in the literature. Experiments demonstrate significant performance gains over baseline models, with ablation studies confirming the critical role of each component in ensuring modeling accuracy. This work establishes a new paradigm for empirical game-theoretic analysis and AI-driven game design.

Technology Category

• Game Theory and Economic Paradigms: Imperfect Information
• Multiagent Systems: Mechanism Design
• Humans and AI: Game Design — Procedural Content Generation & Storytelling

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• User Modeling, Personalization and Recommendation: Large Language Models (LLM) for user modeling and recommendation

Abstract

We introduce a framework for translating game descriptions in natural language into extensive-form representations in game theory, leveraging Large Language Models (LLMs) and in-context learning. Given the varying levels of strategic complexity in games, such as perfect versus imperfect information, directly applying in-context learning would be insufficient. To address this, we introduce a two-stage framework with specialized modules to enhance in-context learning, enabling it to divide and conquer the problem effectively. In the first stage, we tackle the challenge of imperfect information by developing a module that identifies information sets along and the corresponding partial tree structure. With this information, the second stage leverages in-context learning alongside a self-debugging module to produce a complete extensive-form game tree represented using pygambit, the Python API of a recognized game-theoretic analysis tool called Gambit. Using this python representation enables the automation of tasks such as computing Nash equilibria directly from natural language descriptions. We evaluate the performance of the full framework, as well as its individual components, using various LLMs on games with different levels of strategic complexity. Our experimental results show that the framework significantly outperforms baseline models in generating accurate extensive-form games, with each module playing a critical role in its success.

Problem

• Natural Language Processing
• Game Theory
• Mathematical Modeling

Innovation

• Two-Step Method
• Game Theoretic Analysis
• PyGambit Integration