Large language models (LLMs) have recently demonstrated strong capability in understanding and simulating humans’ decisions, suggesting a new way to use LLMs as tools to study social systems. We study two-sided-matching markets, such as dating and job matching. Classical matching models assume deterministic, strict preferences, which violate real-world setting. We focus on stable matching under stochastic decision behavior and use LLMs to simulate human-like preferences and probabilistic choice patterns. Based on this, we introduce Expected Blocking Pairs (EBP), a continuous measure to quantify stability that generalizes the classic blocking pair notion. We further propose a Hybrid GS–LLM matching method that integrates the celebrated Gale–Shapley (GS) algorithm with probabilistic acceptance decisions. Experiments show that the proposed hybrid method outperforms classical baselines in terms of stability, suggesting that LLMs provide a principled tool for modeling human decisions and for improving robustness of matching under uncertainty.

Public scarce resource allocation plays a crucial role in economics as it directly influences the efficiency and equity in society. Traditional studies including theoretical model-based, empirical study-based and simulation-based methods encounter limitations due to the idealized assumption of complete information and individual rationality, as well as constraints posed by limited available data. In this work, we propose an innovative framework, SRAP-Agent, which integrates Large Language Models (LLMs) into economic simulations, aiming to bridge the gap between theoretical models and real-world dynamics. Using public housing allocation scenarios as a case study, we conduct extensive policy simulation experiments to verify the feasibility and effectiveness of the SRAP-Agent and employ the Policy Optimization Algorithm with certain optimization objectives. The source code can be found in https://github.com/jijiarui-cather/SRAPAgent_Framework.