Discovering Expert-Level Nash Equilibrium Algorithms with Large Language Models

• URL: http://arxiv.org/abs/2508.11874v1
• Date: Sat, 16 Aug 2025 02:18:43 GMT
• Title: Discovering Expert-Level Nash Equilibrium Algorithms with Large Language Models
• Authors: Hanyu Li, Dongchen Li, Xiaotie Deng,
• Abstract summary: LegoNE is a framework that fuses the creative process of algorithm design with the rigorous process of formal analysis.<n>Using LegoNE, a state-of-the-art large language model rediscovered the state-of-the-art algorithm for two-player games within hours.<n>This work demonstrates a new human-machine collaborative paradigm for theoretical science.
• Score: 8.041049362762593
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Algorithm design and analysis is a cornerstone of computer science, but it confronts a major challenge. Proving an algorithm's performance guarantee across all inputs has traditionally required extensive and often error-prone human effort. While AI has shown great success in finding solutions to specific problem instances, automating the discovery of general algorithms with such provable guarantees has remained a significant barrier. This challenge stems from the difficulty of integrating the creative process of algorithm design with the rigorous process of formal analysis. To address this gap, we propose LegoNE, a framework that tightly fuses these two processes for the fundamental and notoriously difficult problem of computing approximate Nash equilibria. LegoNE automatically translates any algorithm written by a simple Python-like language into a constrained optimization problem. Solving this problem derives and proves the algorithm's approximation bound. Using LegoNE, a state-of-the-art large language model rediscovered the state-of-the-art algorithm for two-player games within hours, a feat that had taken human researchers 15 years to achieve. For three-player games, the model discovered a novel algorithm surpassing all existing human-designed ones. This work demonstrates a new human-machine collaborative paradigm for theoretical science: humans reason at a higher-abstract level, using symbols to compress the search space, and AI explores within it, achieving what neither could alone.

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