基于访谈的匹配市场偏好获取：离线基准研究
Preference Elicitation in Matching Markets via Interviews: A Study of Offline Benchmarks
摘要：
稳定婚姻问题及其扩展已经被广泛研究，文献中的许多工作都假设代理人完全知道自己对替代品的偏好。然而，这一假设并不总是实用的（特别是在大型市场），代理商通常需要经过一些昂贵的审议过程，以了解他们的偏好。在本文中，我们假设这样的审议是通过采访，其中采访涉及一个男人和一个女人，每个人都了解对方的信息作为一个结果。如果每个人都采访其他人，那么很明显，代理人可以完全了解他们的偏好。但面谈费用很高，我们不妨尽量减少面谈。通常情况下，特别是在实际环境中，由于代理人偏好之间的相关性，为了获得稳定的匹配，没有必要进行所有潜在的访谈。因此，问题是要找到一个很好的策略进行采访，以尽量减少其使用，同时导致稳定的匹配。评估面试策略性能的一种方法是将其与进行所有面试的朴素算法进行比较。然而，我们认为，一个更有意义的比较将是对一个最佳的离线算法，可以访问代理的偏好排序下的完整信息。我们表明，除非P=NP，没有离线算法可以计算的最佳采访策略在多项式时间。如果我们还针对特定的稳定匹配（也许是具有某些理想属性的匹配），我们提供了限制设置，在这些设置下存在有效的最佳离线算法。
英文摘要：
The stable marriage problem and its extensions have been extensively studied, with much of the work in the literature assuming that agents fully know their own preferences over alternatives. This assumption however is not always practical (especially in large markets) and agents usually need to go through some costly deliberation process in order to learn their preferences. In this paper we assume that such deliberations are carried out via interviews, where an interview involves a man and a woman, each of whom learns information about the other as a consequence. If everybody interviews everyone else, then clearly agents can fully learn their preferences. But interviews are costly, and we may wish to minimize their use. It is often the case, especially in practical settings, that due to correlation between agents' preferences, it is unnecessary for all potential interviews to be carried out in order to obtain a stable matching. Thus the problem is to find a good strategy for interviews to be carried out in order to minimize their use, whilst leading to a stable matching. One way to evaluate the performance of an interview strategy is to compare it against a naive algorithm that conducts all interviews. We argue however that a more meaningful comparison would be against an optimal offline algorithm that has access to agents' preference orderings under complete information. We show that, unless P=NP, no offline algorithm can compute the optimal interview strategy in polynomial time. If we are additionally aiming for a particular stable matching (perhaps one with certain desirable properties), we provide restricted settings under which efficient optimal offline algorithms exist.
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。
