We study the problem of allocating a set of objects, e.g. houses, tasks, offices to a group of people having preferences over these objects. For various reasons, it often happens that more objects, sometimes fewer objects are available than initially planned and allocated. How should such...

We study two-sided matching where one side (colleges) can make monetary transfers (offer stipends) to the other (students). Colleges have fixed budgets and strict preferences over sets of students. One different feature of our model is that colleges value money only to the extent that it allows...

We study many-to-one matching with complementarities. Real life examples include college admissions with two-sided monetary transfers, teacher assignment with different teaching loads, worker assignment. Due to the presence of complementarities, the conditions that are essential for the...