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...

This paper studies the problem of assigning a set of indivisible objects to a set of agents when monetary transfers are not allowed and agents reveal only ordinal preferences, but random assignments are possible. We offer two characterizations of the probabilistic serial mechanism, which assigns...

A new mechanism was introduced in New York City and Boston to assign students to public schools. This mechanism was advocated for its superior fairness property, besides others. We introduce a new framework for school-choice problems and two notions of fairness in lottery design based on ex-ante...

Public school systems generally use one of the three competing mechanisms – the Boston mechanism, the deferred acceptance mechanism and the top trading cycle mechanism – for assigning students to specific schools. Although the literature generally claims that the Boston mechanism is Pareto...

We study resource allocation with multi-unit demand, such as the allocation of courses to students. In contrast to the case of single-unit demand, no stable mechanism, not even the (student-proposing) deferred acceptance algorithm, achieves desirable properties: it is not strategy-proof and the...

This paper inspires from a real-life assignment problem faced by the Mexican Ministry of Public Education. We introduce a dynamic school choice problem that consists in assigning positions to overlapping generations of teachers. From one period to another, teachers can either retain their...

We introduce the notion of group robust stability which requires robustness against a combined manipulation, first misreporting preferences and then rematching, by any group of students in the school choice type of matching markets. Our first result shows that there is no group robustly stable...

The absence of simultaneous cycles is a sufficient condition for the existence of singleton cores. Acyclicity in the preferences of either side of the market is a minimal condition that guarantees the existence of singleton cores.

A common real-life problem is to fairly allocate a number of indivisible objects and a fixed amount of money among a group of agents. Fairness requires that each agent weakly prefers his consumption bundle to any other agent's bundle. In this context, fairness is incompatible with budget-balance...