Matching Markets Meet LLMs: Algorithmic Reasoning with Ranked Preferences
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| Format: | Preprint |
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2025
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| _version_ | 1866911305763389440 |
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| author | Hosseini, Hadi Khanna, Samarth Singh, Ronak |
| author_facet | Hosseini, Hadi Khanna, Samarth Singh, Ronak |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_04478 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Matching Markets Meet LLMs: Algorithmic Reasoning with Ranked Preferences Hosseini, Hadi Khanna, Samarth Singh, Ronak Artificial Intelligence Computer Science and Game Theory Theoretical Economics I.2.6; I.2.11; J.4 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. |
| title | Matching Markets Meet LLMs: Algorithmic Reasoning with Ranked Preferences |
| topic | Artificial Intelligence Computer Science and Game Theory Theoretical Economics I.2.6; I.2.11; J.4 |
| url | https://arxiv.org/abs/2506.04478 |