We study iterated matching of soulmates [IMS] — the process of matching coalitions that are the favorite for each member (soulmates), coalitions of soulmates in the remaining group, and so on. Coalitions produced by IMS belong to any stable partition and mechanisms that implement IMS give players in these coalitions (or who at least believe they are) no incentive to deviate from truthful preference reporting, even jointly. When everyone is matched by IMS, these mechanisms are stable and have a truthful strong Nash equilibrium. Furthermore, we show, using real-world data and simulation, that scenarios in which many people are matched by IMS are common under natural kinds of preferences.
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