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 problem of locating a single public good along a segment when agents have single-dipped preferences. We ask whether there are unanimous and strategy-proof rules for this model. The answer is positive and we characterize all such rules. We generalize our model to allow the set of...

We study problems of allocating objects among people. Some objects may be initially owned and the rest are unowned. Each person needs exactly one object and initially owns at most one object. We drop the common assumption of strict preferences. Without this assumption, it suffices to study...

We study the problem of rationing a divisible good among a group of people. Each person’s preferences are characterized by an ideal amount that he would prefer to receive and a minimum quantity that he will accept: any amount less than this threshold is just as good as receiving nothing at...

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...