I study a model where people can be matched in fractions. That is to say, whether a pair is matched is not a binary matter. They can be matched with some intensity. Each has a fixed availability: the total intensity with which he is matched to his partners. I propose a notion of competitive...

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 study the assignment of objects to people via lotteries. We consider the implementation of solutions that are based only on ordinal preferences over the objects. There are three natural ways of comparing lotteries, each of which corresponds to a different notion of Nash equilibrium. For each...