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The stable marriage problem and its extensions have been extensively studied,with much of the work in the literature assuming that agents fully know theirown preferences over alternatives. This assumption however is not alwayspractical (especially in large markets) and agents usually need to go throughsome costly deliberation process in order to learn their preferences. In thispaper we assume that such deliberations are carried out via interviews, wherean interview involves a man and a woman, each of whom learns information aboutthe other as a consequence. If everybody interviews everyone else, then clearlyagents can fully learn their preferences. But interviews are costly, and we maywish to minimize their use. It is often the case, especially in practicalsettings, that due to correlation between agents' preferences, it isunnecessary for all potential interviews to be carried out in order to obtain astable matching. Thus the problem is to find a good strategy for interviews tobe carried out in order to minimize their use, whilst leading to a stablematching. One way to evaluate the performance of an interview strategy is tocompare it against a naive algorithm that conducts all interviews. We arguehowever that a more meaningful comparison would be against an optimal offlinealgorithm that has access to agents' preference orderings under completeinformation. We show that, unless P=NP, no offline algorithm can compute theoptimal interview strategy in polynomial time. If we are additionally aimingfor a particular stable matching (perhaps one with certain desirableproperties), we provide restricted settings under which efficient optimaloffline algorithms exist.

Preference Elicitation in Matching Markets via Interviews: A Study of Offline Benchmarks