优先中性匹配格的特征化
Characterization of Priority-Neutral Matching Lattices
AI总结：
本文研究了优先中性匹配格的结构，证明其比稳定匹配格更复杂，并提出了首个多项式时间算法检查优先中性。
摘要：
我们研究了优先中性匹配集合的结构。这些匹配，由Reny（AER，2022）引入，通过一种有原则的方式允许优先权的违反，从而能够实现对稳定匹配的帕累托改进。已知结果表明，优先中性匹配的集合是一个格，这表明这些匹配可能享有与稳定匹配相同的可处理的理论结构。在本文中，我们特征化了优先中性匹配格，并展示其结构比稳定匹配格更为复杂。首先，我们证明优先中性格不是分布的，这是一个重要的性质，它特征化了稳定格，并且被许多其他匹配理论和算法设计中考虑的格结构所满足。然后，在我们的主要结果中，我们证明优先中性格实际上由一个更为复杂的性质所特征化，我们称之为“移动格”，这允许显著偏离分布（以及因此稳定）格的序论性质。尽管我们的结果表明优先中性比稳定性更复杂，但它们也建立了可处理的性质。确实，作为我们主要结果的推论，我们获得了首个已知的多项式时间算法，用于检查给定匹配是否为优先中性。
英文摘要：
We study the structure of the set of priority-neutral matchings. These matchings, introduced by Reny (AER, 2022), generalize stable matchings by allowing for priority violations in a principled way that enables Pareto-improvements to stable matchings. Known results show that the set of priority-neutral matchings is a lattice, suggesting that these matchings may enjoy the same tractable theoretical structure as stable matchings. In this paper, we characterize priority-neutral matching lattices, and show that their structure is considerably more intricate than that of stable matching lattices. To begin, we show priority-neutral lattices are not distributive, an important property that characterizes stable lattices and is satisfied by many other lattice structures considered in matching theory and algorithm design. Then, in our main result, we show that priority-neutral lattices are in fact characterized by a more-involved property which we term being a "movement lattice," which allows for significant departures from the order theoretic properties of distributive (and hence stable) lattices. While our results show that priority-neutrality is more intricate than stability, they also establish tractable properties. Indeed, as a corollary of our main result, we obtain the first known polynomial-time algorithm for checking whether a given matching is priority-neutral.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
