AI 中文总结
该研究将优先级中性匹配拓展至室友问题，证明了受限室友问题中无阻塞匹配的存在性、其与稳定匹配和帕累托最优匹配的包含关系，还拓展了该概念至双边择校问题。
AI 中文摘要
我们将Reny（2022）在择校情境中提出的优先级中性匹配概念拓展至室友问题。我们证明了三个主要结果：第一，在任意可行性约束下的受限室友问题中，始终存在无阻塞匹配（定理1）；第二，稳定匹配集合包含于无阻塞匹配集合，而无阻塞匹配集合又包含于帕累托最优匹配集合（定理2）；第三，当稳定匹配存在时，无阻塞匹配集合与稳定匹配集合完全重合（定理3）。我们还表明，在弱偏好下该存在性不成立，并将该概念拓展至双边择校问题。
英文摘要
We extend the concept of priority-neutral matching, introduced by Reny (2022) in the school choice context, to the roommate problem. We prove three main results. First, a blocking-neutral matching always exists in constrained roommate problems under arbitrary feasibility constraints (Theorem 1). Second, the set of stable matchings is contained in the set of blocking-neutral matchings, which in turn is contained in the set of Pareto-optimal matchings (Theorem 2). Third, whenever stable matchings exist, the set of blocking-neutral matchings coincides with the set of stable matchings (Theorem 3). We also show that existence fails under weak preferences and extend the concept to two-sided school choice.
