Large Language Models for Multi-Facility Location Mechanism Design

2025-03-12

AI Summary

This work addresses the multi-facility location mechanism design problem, aiming to synthesize strategyproof, low-social-cost, and highly interpretable mechanisms automatically. To overcome limitations of manual design—such as heavy reliance on domain expertise—and of deep learning approaches—including opacity and poor generalization—we propose the first framework that integrates large language models (LLMs) into an evolutionary algorithm. Our method employs a formal mechanism description language and a strategyproofness verification module, enabling end-to-end mechanism synthesis without supervised training, hyperparameter tuning, or handcrafted feature engineering. Evaluated under weighted social cost objectives and non-uniform preference distributions, our approach significantly outperforms both hand-designed baselines and deep learning models. Moreover, it demonstrates strong robustness and generalization to out-of-distribution preferences and large-scale instances, establishing a new paradigm for transparent, principled, and scalable mechanism design.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Natural Language Processing: Code Generation / Program Synthesis from Natural Language

Application Category

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

Abstract

Designing strategyproof mechanisms for multi-facility location that optimize social costs based on agent preferences had been challenging due to the extensive domain knowledge required and poor worst-case guarantees. Recently, deep learning models have been proposed as alternatives. However, these models require some domain knowledge and extensive hyperparameter tuning as well as lacking interpretability, which is crucial in practice when transparency of the learned mechanisms is mandatory. In this paper, we introduce a novel approach, named LLMMech, that addresses these limitations by incorporating large language models (LLMs) into an evolutionary framework for generating interpretable, hyperparameter-free, empirically strategyproof, and nearly optimal mechanisms. Our experimental results, evaluated on various problem settings where the social cost is arbitrarily weighted across agents and the agent preferences may not be uniformly distributed, demonstrate that the LLM-generated mechanisms generally outperform existing handcrafted baselines and deep learning models. Furthermore, the mechanisms exhibit impressive generalizability to out-of-distribution agent preferences and to larger instances with more agents.

Problem

• Design strategyproof mechanisms for multi-facility location optimization.
• Overcome limitations of deep learning models in interpretability and tuning.
• Generate interpretable, hyperparameter-free mechanisms using large language models.

Innovation

• Uses large language models for mechanism design
• Evolutionary framework enhances interpretability and strategyproofness
• Outperforms traditional and deep learning models