We study the marriage problem where a probability distribution over matchings is chosen. The “core” has been central to the the analysis of the deterministic problem. This is particularly the case since it coincides with the (conceptually) simpler set of “stable” matchings. While the...

We consider school choice problems (Abdulkadiroglu and Sönmez, 2003) where students are assigned to public schools through a centralized assignment mechanism. We study the family of so-called rank-priority mechanisms, each of which is induced by an order of rank-priority pairs. Following the...