发表机构
Instituto de Matemática Aplicada San Luis (UNSL-CONICET); Universidad Nacional de San Luis（圣路易斯应用数学研究所; 圣路易斯国立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过推广经典分解引理，揭示了内部稳定性与匹配市场循环结构之间的联系，并基于约简环境的核心唯一刻画了冯·诺伊曼-摩根斯坦稳定集。
AI 中文摘要
本文研究一对一匹配市场中冯·诺伊曼-摩根斯坦（vNM）稳定集的结构与计算。在严格偏好下，成对稳定性和核心稳定性一致，并提供了易于理解的基准，而vNM稳定性通过匹配集之间的支配关系定义，其刻画仍然相当困难。本文的一个关键贡献是经典分解引理的推广。我们证明，传统上用于比较稳定匹配的结构分解可以扩展到属于同一内部稳定集的任意一对匹配。这一结果揭示了内部稳定性与匹配市场底层循环结构之间先前未被探索的联系。基于这一特征刻画，我们识别出与基于支配的稳定性相关的关系，并推导出一个集中所有非支配结果的约简环境。我们的主要结果表明，vNM稳定集是唯一的，并且在该约简环境的核心方面具有简单的刻画。该刻画既提供了结构性洞见，也提供了使用标准匹配理论工具计算vNM稳定集的构造性程序。
英文摘要
This paper studies the structure and computation of von Neumann-Morgenstern (vNM) stable sets in one-to-one matching markets. While pairwise stability and corewise stability coincide under strict preferences and provide a well-understood benchmark, vNM stability is defined through dominance relations among sets of matchings and remains considerably more difficult to characterize. A key contribution of the paper is a generalization of the classical Decomposition Lemma. We show that the structural decomposition traditionally used to compare stable matchings extends to any pair of matchings belonging to the same internally stable set. This result reveals a previously unexplored connection between internal stability and the cycle structure underlying matching markets. Building on this characterization, we identify the relationships that are relevant for dominance-based stability and derive a reduced environment that concentrates all undominated outcomes. Our main result shows that the vNM stable set is unique and admits a simple characterization in terms of the core of this reduced environment. The characterization provides both structural insight and a constructive procedure for computing the vNM stable set using standard matching theoretic tools.
