重新审视夫妻配对
Matching with Couples Revisited
摘要：
众所周知，在多对一配对市场中，稳定的配对不一定存在。我们引入了一个新的匹配算法，这样的市场，并表明，对于一般类的大型随机市场的算法将找到一个稳定的匹配概率很高。特别是，我们允许夫妇的数量以接近线性的速度增长。此外，说实话是一个近似的均衡在游戏中诱导的新的匹配算法。我们的结果很紧凑：对于市场中的夫妇的数量以线性速度增长，我们表明，与常数概率不存在稳定的匹配。
英文摘要：
It is well known that a stable matching in a many-to-one matching market with couples need not exist. We introduce a new matching algorithm for such markets and show that for a general class of large random markets the algorithm will find a stable matching with high probability. In particular we allow the number of couples to grow at a near-linear rate. Furthermore, truth-telling is an approximated equilibrium in the game induced by the new matching algorithm. Our results are tight: for markets in which the number of couples grows at a linear rate, we show that with constant probability no stable matching exists.
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。
