Matching Markets Meet LLMs: Algorithmic Reasoning with Ranked Preferences

Understand

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.