Matching Markets Meet LLMs: Algorithmic Reasoning with Ranked Preferences

TL;DR

This paper evaluates how well large language models handle ranked preferences in matching markets, revealing their limitations in logical reasoning and algorithmic execution, especially in large-scale scenarios.

Contribution

It systematically assesses LLMs on preference-based matching tasks, exposing their reasoning gaps and demonstrating the impact of fine-tuning techniques across different market sizes.

Findings

Top models struggle with instability detection in large markets

Parameter-efficient fine-tuning improves small market performance

Large markets pose significant challenges for LLM reasoning in matching algorithms

Abstract

The rise of Large Language Models (LLMs) has driven progress in reasoning tasks -- from program synthesis to scientific hypothesis generation -- yet their ability to handle ranked preferences and structured algorithms in combinatorial domains remains underexplored. We study matching markets, a core framework behind applications like resource allocation and ride-sharing, which require reconciling individual ranked preferences to ensure stable outcomes. We evaluate several state-of-the-art models on a hierarchy of preference-based reasoning tasks -- ranging from stable-matching generation to instability detection, instability resolution, and fine-grained preference queries -- to systematically expose their logical and algorithmic limitations in handling ranked inputs. Surprisingly, even top-performing models with advanced reasoning struggle to resolve instability in large markets, often failing to identify blocking pairs or execute algorithms iteratively. We further show that parameter-efficient fine-tuning (LoRA) significantly improves performance in small markets, but fails to bring about a similar improvement on large instances, suggesting the need for more sophisticated strategies to improve LLMs' reasoning with larger-context inputs.